Publishing type：Research paper (scientific journal)  

DOI： 10.1093/ptep/ptad156

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Authorship：Last author   Publishing type：Research paper (scientific journal)  

DOI： 10.1103/PhysRevB.106.134304

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Authorship：Lead author,　Corresponding author   Publishing type：Research paper (scientific journal)   Publisher：Physical Society of Japan  

DOI： 10.7566/jpsj.91.062001

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Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

DOI： 10.1103/physrevb.105.014417

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevB.105.014417/fulltext

Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We propose an entanglement-based algorithm of the tensor-network strong-disorder renormalization group (tSDRG) method for quantum spin systems with quenched randomness. In contrast to the previous tSDRG algorithm based on the energy spectrum of renormalized block Hamiltonians, we directly utilize the entanglement structure associated with the blocks to be renormalized. We examine accuracy of the algorithm for the random antiferromagnetic Heisenberg models on one-dimensional, triangular, and square lattices. We then find that the entanglement-based tSDRG achieves better accuracy than the previous one for the square-lattice model with weak randomness, while it is less efficient for the one-dimensional and triangular-lattice models particularly in the strong-randomness region. The theoretical background and possible improvements of the algorithm are also discussed.

DOI： 10.1103/PhysRevB.104.134405

Web of Science

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Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s00723-020-01296-w

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Other Link： https://link.springer.com/article/10.1007/s00723-020-01296-w/fulltext.html

Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society ({APS})  

DOI： 10.1103/physrevb.102.144439

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Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

DOI： 10.1103/physreve.101.062111

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevE.101.062111/fulltext

Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

We investigate the phase transition of the dodecahedron model on the square lattice. The model is a discrete analogue of the classical Heisenberg model, which has continuous $O(3)$ symmetry. In order to treat the large on-site degree of freedom $q = 20$, we develop a massively parallelized numerical algorithm for the corner transfer matrix renormalization group method, incorporating EigenExa, the high-performance parallelized eigensolver. The scaling analysis with respect to the cutoff dimension reveals that there is a second-order phase transition at $T^{~}_{\rm c}=0.4398(8)$ with the critical exponents $\nu=2.88(8)$ and $\beta=0.21(1)$. The central charge of the system is estimated as $c=1.99(6)$.

DOI： 10.1103/physreve.102.0321

DOI： 10.1103/PhysRevE.102.032130

arXiv

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevE.102.032130/fulltext

Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.7566/jpsj.88.114002

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Bentham Science Publishers Ltd.  

<sec>
<title>Background:</title>
In this paper, we report on the topics of one-dimensional (1D) and two-dimensional
(2D) functional materials. Single-Walled Carbon Nanotubes (SWCNTs) are seamless hollow cylinders made of
hexagonal lattice graphite sheets. The SWCNTs have attracted considerable attention due to the applicability of
their enclosed nanospaces to engineering, and many types of guest materials are encapsulated inside their 1D
space, expecting unusual properties. The poly Transition Metal (TM) phthalocyanine, in which phthalocyanine
units are extended in two dimensions by sharing benzene rings, is one of the examples of the TM containing 2D
carbon materials. Because of strong correlation between localized d-electrons in the TM atom and delocalized
π-electrons on the poly phthalocyanine frame, it is expected that spin-polarized conduction, which is useful for
the spintronic applications.


</sec>
<sec>
<title>Objectives:</title>
The objective of the first work is to synthesize SWCNTs encapsulating oxygen molecules having
spin one, whose O-O bond directions are aligned to the longitudinal direction of the SWCNTs. The objective of
the second work is to synthesize Poly Cu Phthalocyanine (PCuPc) through a bottom-up method by using copper
octacyanophthalocyanine as a building block and to elucidate its crystal structure and magnetic properties.



</sec>
<sec>
<title>Methods:</title>
SWCNTs with inner diameter of ca 0.8 nm were prepared by the CoMoCAT method, and encapsulated together with oxygen molecules (~400 Torr) into a high-purity quartz tube. To subtract the background signals of the SWCNTs and the quartz tube, we prepared the same SWCNTs inducing He gas after evacuating oxygen molecules. Magnetization measurements of these SWCNTs samples were conducted by means of a SQUID magnetometer and a pulse magnet using an induction method. PCuPc were synthesized by a solid state reaction of octacyanophthalocyanine, tetracyanobenzene, and CuCl₂·2H₂O in glass ampoules sealed after evacuation. The as-synthesized samples were characterized using XRD analysis and TEM microscopy. Magnetization measurement of the samples were done by using a SQUID magnetometer.


</sec>
<sec>
<title>Results:</title>
The intrinsic magnetization data from oxygen molecules inside the SWCNTs (temperature and magnetic field dependence) show magnetic properties typical of the spin-one Heisenberg antiferromagnet named a Haldane magnet. PCuPc and its half-filling counterpart were obtained by solid state reaction. Both magnetic susceptibility and magnetization of PCuPc are larger than those of half-filling PCuPc, but the magnitudes of the former sample are about 1.5 times larger than those of the latter one, which is expected to be twice from the geometric superlattice structure.


</sec>
<sec>
<title>Conclusion:</title>
We have studied magnetic properties (magnetic susceptibility and magnetization) of oxygen molecules encapsulated into Single Walled Carbon Nanotubes (SWCNTs) with diameters of about 0.8 nm, regarded as a 1D functional magnetic material, and Poly Copper Phthalocyanine (PCuPc) and poly half-filling copper phthalocyanine (half-filling PCuPc), regarded as 2D functional magnetic materials.


</sec>

DOI： 10.2174/1874842201906010027

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Other Link： https://openchemistryjournal.com/contents/volumes/V6/CHEM-6-27/CHEM-6-27.xml

Language：Japanese   Publisher：The Physical Society of Japan  

DOI： 10.11316/jpsgaiyo.74.2.0_2339

CiNii Article

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Language：Japanese   Publisher：The Physical Society of Japan  

DOI： 10.11316/jpsgaiyo.74.2.0_2341

CiNii Article

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Publishing type：Research paper (scientific journal)  

We study low-energy properties of the S=1/2 kagome-triangular-strip Heisenberg model. Using exact diagonalization, we calculate magnetization curves of the model in the ferromagnetic kagome coupling regime, where the singlet ground state and 1/3 plateau emerge. In order to analyze formation of the singlet ground state, we further derive a low-energy effective ladder model, focusing on the parity degrees of freedom for the two degenerating doublets of the unit triangle. We then discuss the entanglement between the spin and parity degrees of freedom. <P />...

DOI： 10.1063/1.5042702

Web of Science

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Physical Society of Japan  

Alkali superoxide CsO<SUB>2</SUB> is one of the candidates for the spin-1/2 one-dimensional (1D) antiferromagnet, which may be sequentially formed by an ordering of the π-orbital of O<SUB>2</SUB><SUP> - </SUP> molecule below T<SUB>S</SUB> ̃ 70 K. Here, we report the magnetism and the high-magnetic field magnetization in pulsed-magnetic fields up to 60 T in powder CsO<SUB>2</SUB>. We obtained the low temperature phase diagram around the antiferromagnetic ordering temperature T<SUB>N</SUB> = 9.6 K under the magnetic field. At T = 1.3 K, we observed a remarkable up-turn curvature in the magnetization around a saturation field of ̃60 T, which indicates the low-dimensional nature of the spin system. The saturated magnetization is also estimated to be ̃1μ<SUB>B</SUB>, which corresponds to spin-1/2. In this study we compare it with the theoretical calculation. <P />...

DOI： 10.7566/JPSJ.87.063704

Web of Science

Scopus

arXiv

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

In the context of a discrete analog of the classical Heisenberg model, we investigate the critical behavior of the icosahedron model, where the interaction energy is defined as the inner product of neighboring vector spins of unit length pointing to the vertices of the icosahedron. The effective correlation length and magnetization of the model are calculated by means of the corner-transfer-matrix renormalization group (CTMRG) method. A scaling analysis with respect to the cutoff dimension m in CTMRG reveals a second-order phase transition characterized by the exponents ν =1.62 ±0.02 and β =0.12 ±0.01 . We also extract the central charge from the classical analog of entanglement entropy as c =1.90 ±0.02 , which cannot be explained by the minimal series of conformal field theory. <P />...

DOI： 10.1103/PhysRevE.96.062112

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arXiv

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

The coupled spin tube system, which is equivalent to a stacked Kagome-triangular spin system, exhibits the cuboc order — a non-coplanar spin order with a twelve-sublattice structure accompanying spontaneous breaking of the translational symmetry — in the Kagome-triangular plane. On the basis of the spin-wave theory, we analyze spin-wave excitations of the planar Kagome-triangular spin system, where the geometric phase characteristic to the cuboc spin structure emerges. We further investigate spin-wave excitations and dynamical spin structure factors for the coupled spin tubes, assuming the staggered cuboc order. <P />...

DOI： 10.7566/JPSJ.86.114701

Web of Science

arXiv

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

BaCo<SUB>2</SUB>V<SUB>2</SUB>O<SUB>8</SUB> consists of Co chains in which a Co<SUP>2 +</SUP> ion carries a fictitious spin 1/2 with Ising anisotropy. We performed elastic and inelastic neutron scattering experiments in BaCo<SUB>2</SUB>V<SUB>2</SUB>O<SUB>8</SUB> in a magnetic field perpendicular to the c axis which is the chain direction. With applying magnetic field along the a axis at 3.5 K, the antiferromagnetic order with the easy axis along the c axis, observed in zero magnetic field, is completely suppressed at 8 T, while the magnetic field gradually induces an antiferromagnetic order with the spin component along the b axis. We also studied magnetic excitations as a function of transverse magnetic field. The lower boundary of the spinon excitations splits gradually with increasing magnetic field. The overall feature of the magnetic excitation spectra in the magnetic field is reproduced by the theoretical calculation based on the spin 1/2 X X Z antiferromagnetic chain model, which predicts that the dynamic magnetic structure factor of the spin component along the chain direction is enhanced and that along the field direction has clear incommensurate correlations. <P />...

DOI： 10.1103/PhysRevB.96.024439

Web of Science

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Publishing type：Research paper (scientific journal)   Publisher：arXiv e-prints  

We introduce a snapshot density matrix and snapshot spectrum for world-line (WL) quantum Monte Carlo simulations, by integrating out the continuous-imaginary-time index of WL snapshots. For the transverse-field Ising chain, we reveal fundamental properties of the snapshot spectrum as follows. (i) In the ordered phase, the isolated peak corresponding to the maximum eigenvalue appears, indicating the classical nature of WL configurations. (ii) In the disordered phase, the spectrum converges to the dome-like distribution characterized by an effective aspect ratio of the snapshots. (iii) At the critical point, the power-law distribution is observed with an appropriate scaling analysis of the fixed aspect ratio. For the XXZ chain, we also obtain numerical results consistent with the above properties. In addition, the representation-basis dependence of the snapshot spectrum is also discussed. <P />...

DOI： 10.7566/JPSJ.88.024003

Web of Science

arXiv

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We investigate the sine-square deformation (SSD) of free fermions in one-dimensional continuous space. On the basis of supersymmetric quantum mechanics, we prove the correspondence between the many-body ground state of the system with SSD and that of the uniform system with periodic boundary conditions. We also discuss the connection between the SSD in the continuous space and its lattice version, where the geometric correction due to the real-space deformation plays an important role in relating the eigenstates of the lattice SSD with those of the continuous SSD. <P />...

DOI： 10.1088/1751-8113/48/44/445208

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arXiv

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

We report on the results of magnetic susceptibility and high field magnetization measurements on single crystals of SrCo<SUB>2</SUB>V<SUB>2</SUB>O<SUB>8</SUB>, which is regarded as an S = 1/2 quasi one-dimensional Ising-like antiferromagnet and is almost isostructural to BaCo<SUB>2</SUB>V<SUB>2</SUB>O<SUB>8</SUB> that has exhibited a field-induced order-to-disorder transition. The magnetization measurements have been performed at 1.4 K below the Néel temperature T<SUB>N</SUB> = 4.8 K in pulsed fields of up to 50 T. The temperature dependence of magnetic susceptibility parallel to the c-axis (chain axis) has a broad maximum near 40 K, which is typical of a low dimensional antiferromagnet, while the susceptibilities perpendicular to the c-axis do not show such a maximum. The magnetization at 1.9 K along the c-axis shows a steep increase at 3.8 T as in BaCo<SUB>2</SUB>V<SUB>2</SUB>O<SUB>8</SUB>, corresponding to the field-induced order-to-disorder transition. The magnetization curve along the c-axis up to the saturation magnetization is well fitted to the magnetization curve calculated by the exact solution based on the Bethe ansatz for an S = 1/2 XXZ model, and this analysis provides parameter values for the exchange constant J/k<SUB>B</SUB> = 78 K, the anisotropic exchange parameter ∊ = 0.50, and the g-value along the c-axis g<SUB>c</SUB> = 6.1. In contrast, the magnetization curves perpendicular to the c-axis show gradual increase up to 50 T. <P />...

DOI： 10.1016/j.phpro.2015.12.101

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

We investigate the eigenvalue distribution of the snapshot density matrix (SDM) generated by Monte Carlo simulation for two-dimensional classical spin systems. We find that the distribution in the high-temperature limit is well explained by the random-matrix theory, while that in the low-temperature limit can be characterized by the zero-eigenvalue condensation. At the critical point, we obtain the power-law distribution with a nontrivial exponent α ≡ (2 - η)/(1 - η) and the asymptotic form of the snapshot entropy, on the basis of the relationship of the SDM with the correlation function matrix. The aspect-ratio dependence of the SDM spectrum is also mentioned. <P />...

DOI： 10.7566/JPSJ.83.114002

Web of Science

arXiv

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

We report on the results of X-ray diffraction (XRD), magnetic susceptibility, and high-field magnetization measurements of oxygen molecules, which are unique magnetic homonuclear diatomic molecules with spin-1, encapsulated in single-walled carbon nanotubes (SWCNTs) with diameters of about 0.8 nm. Antiferromagnetic interactions between neighboring oxygen molecules are expected in SWCNTs, resulting in the formation of a spin-1 one-dimensional Heisenberg antiferromagnet, known as a Haldane magnet. The XRD pattern can be predicted accurately by considering the expected oxygen molecule alignment. The temperature evolution of the magnetic susceptibility and the high-field magnetization curve are typical of those for a Haldane magnet with spin-1. The results indicate that the Haldane state has been realized in a nanospaced material for the first time. This provides an alternative to the conventional condensed matter approach to forming quantum spin systems. <P />...

DOI： 10.7566/JPSJ.83.113706

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Using a generalized Jordan-Wigner transformation combined with the defining representation of the SO(N) spin, we map the SO(N) bilinear-biquadratic (BLBQ) spin chain into the N-color bosonic particle model. We find that, when the Jordan-Wigner transformation disentangles the symmetry-protected topological entanglement, this bosonic model becomes negative-sign-free in the context of quantum Monte Carlo simulation. For the SO(3) case, moreover, the Kennedy-Tasaki transformation for the S =1 BLBQ chain, which is also a topological disentangler, derives the same bosonic model through the dimer-R bases. We present the temperature dependence of the energy, entropy, and string order parameter for the SO(N =3,4,5) BLBQ chains by a world-line Monte Carlo simulation for the N-color bosonic particle model. <P />...

DOI： 10.1103/PhysRevB.89.134422

Web of Science

arXiv

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

We have succeeded in synthesizing two types of new organic radical crystals 3-I-V [= 3-(3-iodophenyl)-1,5-diphenylverdazyl] and 3-Br-4-F-V [= 3-(3-bromo-4-fluorophenyl)-1,5-diphenylverdazyl]. Their crystal strucutures are found to be isomorphous to that of previously reported spin ladder 3-Cl-4-F-V. Through the quantitative analysis of their molecular arrangements and magnetic properties, we confirm that these materials form ferromagnetic chain-based spin ladders with slightly modulated magnetic interactions. These results present the first quantitative demonstration of the fine-tuning of magnetic interactions in the molecular-based materials. <P />...

DOI： 10.7566/JPSJ.83.033707

Web of Science

arXiv

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We investigate the entanglement spectrum in HOTRG-tensor renormalization group (RG) method combined with the higher order singular value decomposition-for two-dimensional (2D) classical vertex models. In the off-critical region, it is explained that the entanglement spectrum associated with the RG transformation is described by "doubling" of the spectrum of a corner transfer matrix. We then demonstrate that the doubling actually occurs for the square-lattice Ising model by HOTRG calculations up to D = 64, where D is the cutoff dimension of tensors. At the critical point, we also find that a nontrivial D scaling behavior appears in the entanglement entropy. We mention about the HOTRG for the 1D quantum system as well.

DOI： 10.1103/PhysRevB.89.075116

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

The S=1/2 three-leg spin tube is investigated using the numerical diagonalization up to the 42-spin clusters. A precise finite-size scaling analysis, so called the level spectroscopy, is carried out. It indicates a quantum phase transition between the spin-gap and gapless phases, with respect to the ratio of the leg and rung exchange interactions. The present analysis gives a precise estimate for the critical value of the ratio.

DOI： 10.1088/1742-6596/568/4/042024

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：KOREAN PHYSICAL SOC  

We study quantum phase transitions in the 1/3 plateau state of the three-leg spin-1/2 tube, where the low-energy effective chirality degree of freedom plays an essential role. Using the density matrix renormalization group and the effective chirality model, we find that, as the leg coupling increases, the chirality liquid, a novel spin imbalance phase and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. We also clarify the role of the S (3)-symmetry of the spin tube, behind these quantum phase transitions.

DOI： 10.3938/jkps.63.596

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER/PLENUM PUBLISHERS  

We have performed magnetic susceptibility and high-field magnetization measurements on powder samples of Cu(DEP)Br-2 (DEP=2,3-diethyl-pyrazine) and Cu(DMP)Cl-2 (DMP=2,3-dimethyl-pyrazine) which are regarded as spin-1/2 two-leg spin-ladders in which the exchange constants are given by J (ayen) along the leg and J (aSyen) along the rung. The temperature dependences of magnetic susceptibilities of these compounds show a round peak at 11 and 18 K, respectively, and are compared with those calculated with a density matrix renormalization group method for alpha=J (ayen)/J (aSyen)=0.45-0.55. The exchange constants of the former and the latter compounds are evaluated to be and , respectively. No magnetization at 1.3 K appears in magnetic fields of up to about 5 T for Cu(DEP)Br-2 and about 14 T for Cu(DMP)Cl-2, and then the magnetization increases monotonically to saturate at around 25 T and 38 T for respective compounds. Both magnetization curves are also compared with those calculated for alpha=0.45-0.55 using the same exchange parameter values as in the susceptibilities.

DOI： 10.1007/s10909-012-0809-y

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

We have performed magnetization measurements of the quasi one-dimensional (1D) S = 1/2 Ising-like anti-ferromagnet BaCo2V2O8 in transverse fields. Different from the expectation by the 1D S = 1/2 XXZ model, a steep suppression of the antiferromagnetic order is observed for H parallel to left perpendicular100right perpendicular, whereas the experimental results for H parallel to left perpendicular110right perpendicular agree with the XXZ model. We show that these anisotropic behaviors are caused by a characteristic screw chain structure in BaCo2V2O8, which gives rise to a peculiar angular dependence of effective fields upon application of uniform external magnetic fields.

DOI： 10.7566/JPSJ.82.033706

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

From heat capacity (C-p) measurements on a single crystal sample of the spin (S) 1/2 two-leg spin-ladder material Cu(DEP)Br-2 above a critical magnetic field (H-c0) where the energy gap between the singlet ground state and the excited magnetic state closes, we have observed a peak anomaly, which is indicative of a magnetic long-range ordering. We have examined how the position of the anomaly in C-p changes with temperature (T) and magnetic field (H) to obtain the experimental H-T phase diagram of this S = 1/2 two-leg spin ladder material. From the low-temperature specific heat below H-c0, we have evaluated the field-dependent energy gap that vanishes at about 7.6 T.

DOI： 10.1143/JPSJ.81.113710

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Publisher：arXiv e-prints  

We discuss the relation between the Wilson's numerical renormalization group(NRG) for the Kondo impurity problem and a field theory in the background AdS_3 space time, where the radial coordinate plays a role of the controlling parameter of the effective mass scale. We find that the Wilson NRG can be described by the boundary Rindler field and then the cutoff parameter \lambda of the Wilson NRG is related to the AdS radius L through \lambda = 2k_F/\omega L, where k_F is the effective Fermi wave number. It is also found that the Rindler space is discretized with the lattice space of a=\pi/k_F. <P />...

arXiv

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study the magnetization plateau state of the three-leg spin-1/2 tube in the strong rung coupling region, where S-3 symmetry breaking and the low-energy chirality degree of freedom play crucial roles. On the basis of the effective chirality model and density matrix renormalization group, we clarify that, as the leg coupling increases, the chirality liquid with gapless nonmagnetic excitations, the spin-imbalance phase, and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. The relevance of these results to experiments is also discussed.

DOI： 10.1103/PhysRevB.85.054416

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

Recently some quantum spin systems on tube lattices, so called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As the first step of theoretical study on the spin nanotube, we investigate the S=1/2 three-leg spin tube, which is the simplest one, using the numerical exact diagonalization and the finite-size scaling analysis. In our previous works the quantum phase transition between the spin-gap and gapless phases was revealed to occur due to the asymmetric lattice distortion. In addition the transition between the magnetization plateau and gapless phases at 1/3 of the saturation magnetization induced by the same distortion. Recently we found that the Tomonaga-Luttinger liquid is realized in the 1/3 magnetization plateau phase for the symmetric three-leg spin tube.

DOI： 10.1088/1742-6596/400/3/032075

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

We have performed magnetostriction and ultrasound measurements on the quasi-one-dimensional S = 1/2 Ising-like antiferromagnet BaCo2V2O8 in high magnetic fields of up to 51 T. The magnetostriction shows lattice shrinking along the c-axis, and we interpret it as the lattice distortion caused by exchange striction and Van-Vleck paramagnetism. It is clarified that the field dependence of sound velocity is correlated to the magnetostriction. We observed a pronounced softening in the sound velocity of the longitudinal-acoustic c(33) mode and found a novel phase transition.

DOI： 10.1143/JPSJ.80.033701

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

We study a uniform matrix product state as a variational state for classical and quantum spin chains in the thermodynamic limit. Under careful treatment of the translational symmetry, eigenvalues of the transfer matrix defined in the calculation of expectation values can reflect the periodicity of the ground state and indicate the optimum periodicity of the matrix product state. We discuss the relationship between the periodicity and accuracy of magnetization curves. This approach is free from the error due to finite system size, and works well, especially for the magnetic plateau problem.

DOI： 10.1143/JPSJ.80.023001

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

The S = 1/2 three-leg spin nanotube is theoretically investigated, using the numerical diagonalization and the density matrix renormalization group (DMRG) calculation. The system has a magnetization plateau at 1/3 of the saturation magnetization for sufficiently large rung interaction. We mainly focus on the effect of the asymmetric distortion from the regular triangle to the isosceles one. We find an anomalous increase of the plateau width near the symmetric point (i.e., regular triangle) when the asymmetric parameter is varied. (C) 2010 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.physe.2010.07.047

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Language：English   Publishing type：Research paper (international conference proceedings)  

We report the numerical calculations of the distribution of maximal eigenvalue for various size of random correlation matrices. Such an extensive study enables us to work out empirical formulas for the average and standard deviation of the maximal eigenvalue, which are accurate in a wide range of parameters. As an application of those formulas, we propose a criterion to single out statistically meaningful correlations in the principal component analysis. The new criterion incorporates finite-size effects into the current method based on the random matrix theory, which gives the exact results in the infinite-size limit. © 2011 Springer-Verlag Berlin Heidelberg.

DOI： 10.1007/978-3-642-22194-1_55

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

Recently some quantum spin systems on tube lattices, so called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As the first step of theoretical study on the spin nanotube, we investigate the S=1/2 three-leg spin tube, which is the simplest one, using the numerical exact diagonalization (ED), combined with the recently developed level spectroscopy analysis. Particularly, we introduce the lattice distortion from the regular triangle unit to the isosceles one. We revealed that the S=1/2 isosceles triangle spin tube exhibits the quantum phase transition between the spin gapped and gapless spin liquid phases.

DOI： 10.1088/1742-6596/302/1/012013

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

We investigate the S=1/2 three-leg spin tube, which is the simplest spin nanotube, using the density matrix renormalization group (DMRG) and the numerical exact diagonalization (ED), conbined with a finite-size scaling analysis. Particularly, we intruduce the lattice distortion from the regular triangle unit to the isosceles one. In our previous works, we revealed that the S=1/2 isosceles triangle spin tube exhibits following exotic quantum phenomena: the quantum phase transition between the spin gapped and gapless spin liquid phases, the 1/3 magnetization plateau due to two different mechanisms, and a new phase between the two plateau phases where the translational symmetry is spontaneously broken. We briefly review these results and show our new calculation of the expectation value of the magnetization at each site to specify the spin structure in the new field induced phase.

DOI： 10.1088/1742-6596/320/1/012022

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Language：English   Publishing type：Research paper (scientific journal)  

We discuss the scale-free property of Wilson's numerical renormalization group (NRG) for the Kondo-impurity problem. The single-particle state of the effective Hamiltonian with a cutoff Λ is described by the wave-packet basis having the scale-free property. The energy scale of the system can be controlled by the lattice translation of the wave-packet basis with no reference of rescaling of the lattice space. We also analyze the role of the Kondo interaction in the context of wave-packet basis and then discuss the scaling and renormalization of the Kondo coupling. In addition, we clarify the role of the edge state in the lowest energy scale of Wilson NRG. © 2010 The American Physical Society.

DOI： 10.1103/PhysRevB.82.144409

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Language：English   Publisher：IOP PUBLISHING LTD  

Recent developments of theoretical studies on spin nanotubes are reviewed, especially focusing on the S = 1/2 three-leg spin tube. In contrast to the three-leg spin ladder, the tube has a spin gap in the case of the regular-triangle unit cell when the rung interaction is sufficiently large. The effective theory based on the Hubbard Hamiltonian indicates a quantum phase transition to a gapless spin liquid due to the lattice distortion to an isosceles triangle. This is also supported by the numerical diagonalization and the density matrix renormalization group analyses. Furthermore, combining analytical and numerical approaches, we reveal several novel magnetic-field-induced phenomena: Neel, dimer, chiral and/or inhomogeneous orders, a new mechanism for the magnetization plateau formation, and others. The recently synthesized spin tube materials are also briefly introduced.

DOI： 10.1088/0953-8984/22/40/403201

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We discuss the scale-free property of Wilson's numerical renormalization group (NRG) for the Kondo-impurity problem. The single-particle state of the effective Hamiltonian with a cutoff Lambda is described by the wave-packet basis having the scale-free property. The energy scale of the system can be controlled by the lattice translation of the wave-packet basis with no reference of rescaling of the lattice space. We also analyze the role of the Kondo interaction in the context of wave-packet basis and then discuss the scaling and renormalization of the Kondo coupling. In addition, we clarify the role of the edge state in the lowest energy scale of Wilson NRG.

DOI： 10.1103/PhysRevB.82.144409

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The magnetization process of the S=1/2 three-leg spin tube with an asymmetric exchange interaction in each triangle unit is investigated by the numerical exact diagonalization and the density matrix renormalization group calculation. It is found that the 1/3 magnetization plateau appears due to two different mechanisms depending on the asymmetry. The phase diagrams of the 1/3 plateau is presented. In addition some cusp-like anomalies are found in the magnetization curve.

DOI： 10.1007/s10909-009-0075-9

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We numerically investigate the magnetization process of a frustrated S = 1 chain with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) exchange interactions, which compete with each other, and also with uniaxial single-ion-type anisotropy energies. Special attention is paid to the half magnetization plateau which appears at the half of the saturation magnetization in the ground-state magnetization curve. We determine the parameter region where this plateau appears by employing the level spectroscopy method, and find that the plateau appears even in the absence of the single-ion-type anisotropy, if the ratio of the nnn to the nn interaction constant is in a specified region.

DOI： 10.1088/1742-6596/200/2/022065

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Using Wang-Landau simulation, we investigate the nature of the quasi-one-dimensional(Q1D) Ising model in terms of energy density of states(DOS); In order to treat the large difference of the energy scales between intra-and inter-chain couplings, we particularly introduce DOS in the two dimensional energy space corresponding to the intra-and inter-chain directions, and then discuss size dependence of the peak structure of specific heat. We also analyze the inter-chain coupling dependence of the spin flop transition of the Q1D classical XXZ model with the Ising-like anisotropy using the Wang-Landau simulation.

DOI： 10.1088/1742-6596/200/2/022043

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We report the results of our magnetic susceptibility, magnetization, and multi-frequency electron spin resonance (ESR) measurements on single crystals of the two-leg spin-ladder material Na2Fe2(C2O4)(3)(H2O)(2). Magnetization processes in magnetic fields up 53 T at 1.3 K parallel (H parallel to a) and perpendicular (H perpendicular to a) to the leg direction show a gradual increase compared with those of the isomorphous compound Na2Co2(C2O4)(3)(H2O)(2), which was well explained by an isolated antiferromagnetic dinner model. Thus, we calculated the magnetic susceptibilities and magnetizations on the basis of a two-leg ladder model with a fictitious spin (S) one by a quantum Monte Carlo method and a density-matrix renormalization group method, respectively. These calculated results, however, did not agree well with the experimental ones. Therefore, we regarded Na2Fe2(C2O4)(3)(H2O)(2) as an isolated S = 1 antiferromagnetic dimer with not only the anisotropy of the exchange interactions due to the truncation of spin space but also single-ion anisotropy. Consequently, we obtained good agreement between the experimental and calculated results on the magnetic susceptibilities, magnetizations, ESR resonance modes, and specific heat.

DOI： 10.1143/JPSJ.78.124701

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We study the low-energy excitation of the quantum spin tube with the triangular lattice structure, using density matrix renormalization group. Taking account of the edge spin effect, we particularly investigate the spin gap behavior and the low-field magnetization curve near the quantum phase transition point in contrast with the usual free boundary condition. We then find that the bulk behavior of the spin tube can be extracted easier for the single spin termination.

DOI： 10.1142/S0129183109014485

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We have measured the specific heat of the S = 1/2 alternating-bond Heisenberg antiferromagnetic chain compound pentafluorophenyl nitronyl nitroxide in magnetic fields using a single crystal and powder. A sharp peak due to field-induced magnetic ordering (FIMO) is observed in both samples. The H-T phase boundary of the FIMO of the single crystal is symmetric with respect to the central field of the gapless field region H-C1 &lt;= H &lt;= H-C2, whereas it is distorted for the powder whose ordering temperatures are lower. We discuss possibility that an effective pressure caused by mixing the powder with grease, which is reported for various organic compounds, plays an important role for the distorted phase boundary. An analysis employing calculations based on the finite temperature density matrix renormalization group suggests that the pressure-induced frustration enhances incommensurate spin correlation leading to the distorted phase boundary for the powder.

DOI： 10.1143/JPSJ.78.074716

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We revisit the nature of the quasi-one-dimensional Ising model on the basis of Wang-Landau simulation. We introduce the density of states in the two-dimensional energy space corresponding to the intra- and interchain directions. We then analyze the interchain coupling dependence of specific heat of the anistropic two-dimensional Ising model in the context of the density of states, and further discuss the size dependence of peak temperature. We also discuss the feature of the phase transition in the three-dimensional case.

DOI： 10.1143/JPSJ.78.054002

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DOI： 10.1088/1742-6596/150/4/042090

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We report the results of thermodynamic measurements on the quasi one-dimensional (1D) Ising-like antiferromagnet BaCo2V2O8 in the magnetic fields for H//c down to 200 mK. An appearance of a long range magnetic ordered phase is observed in the field induced region above H-c similar or equal to 3.9 T at temperature below 1.8 K. A peculiar incommensurate ordering, which reflects a quantum critical nature of S = 1/2 1D Ising-like antiferromagnet, realizes in this ordered phase.

DOI： 10.1088/1742-6596/150/4/042090

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We study the ordered state of the quasi-one dimensional S = 1/2 XXZ spin model in magnetic fields by using quantum Monte Carlo simulations based on the directed-loop algorithm. The H-T phase diagram is illustrated and we find that an incommensurate long-range-ordered state is stable in a certain low-magnetized region. The result of the finite-size scaling analysis indicates that the finite temperature transition to the incommensurate order is of the first order.

DOI： 10.1088/1742-6596/150/4/042197

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We investigate quantum phase transitions of the S= 1 2 three-leg antiferromagnetic spin tube with asymmetric interchain (rung) exchange interactions. On the basis of the electron tube system, we propose a useful effective theory to give the global phase diagram of the asymmetric spin tube. In addition, using other effective theories we raise the reliability of the phase diagram. The density-matrix renormalization-group and the numerical diagonalization analyses show that the finite spin gap appears in a narrow region around the rung-symmetric line, in contrast to a recent paper by Nishimoto and Arikawa, [Phys. Rev. B 78, 054421 (2008)]. The numerical calculations indicate that this global phase diagram obtained by use of the effective theories is qualitatively correct. In the gapless phase on the phase diagram, the numerical data are fitted by a finite-size scaling in the c=1 conformal field theory. We argue that all the phase transitions between the gapful and gapless phases belong to the Berezinskii-Kosterlitz-Thouless universality class. © 2008 The American Physical Society.

DOI： 10.1103/PhysRevB.78.184415

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We investigate quantum phase transitions of the S=1/2 three-leg antiferromagnetic spin tube with asymmetric interchain (rung) exchange interactions. On the basis of the electron tube system, we propose a useful effective theory to give the global phase diagram of the asymmetric spin tube. In addition, using other effective theories we raise the reliability of the phase diagram. The density-matrix renormalization-group and the numerical diagonalization analyses show that the finite spin gap appears in a narrow region around the rung-symmetric line, in contrast to a recent paper by Nishimoto and Arikawa, [Phys. Rev. B 78, 054421 (2008)]. The numerical calculations indicate that this global phase diagram obtained by use of the effective theories is qualitatively correct. In the gapless phase on the phase diagram, the numerical data are fitted by a finite-size scaling in the c=1 conformal field theory. We argue that all the phase transitions between the gapful and gapless phases belong to the Berezinskii-Kosterlitz-Thouless universality class.

DOI： 10.1103/PhysRevB.78.184415

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We investigate the ordered state in S = 1/2 XXZ spin chains with weak interchain couplings in a magnetic field by using quantum Monte Carlo simulations based on the directed-loop algorithm. The HT phase diagram is illustrated for a square lattice and we find that an exotic spin-liquid state with quasi long-range incommensurate correlations in both the spin-chain and interchain directions may appear in the low-magnetization region without a finite-temperature transition. We also show that the incommensurate long-range-ordered state is stable for a cubic lattice.

DOI： 10.1143/JPSJ.76.123707

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We investigate phase transitions of the quasi-one-dimensional S=1/2 XXZ model in a magnetic field, using bosonization combined with a mean-field treatment of the interchain interaction. We then find that the field-induced incommensurate order is certainly realized in the low-field region, while transverse staggered order appears in the high-field region. On the basis of the result, we discuss the field-induced phase transition recently observed for BaCo2V2O8.

DOI： 10.1103/PhysRevB.76.224411

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High field magnetization and ESR measurements on the quasi-one-dimensional (1D) antiferromagnet BaCo2V2O8 have been performed in magnetic fields up to 50 T along the chain. The experimental results are explained well in terms of a 1D S=1/2 antiferromagnetic XXZ model in longitudinal fields. We show that the quantum phase transition from the Neel ordered phase to the spin liquid one in the model is responsible for a peculiar order to disorder transition in BaCo2V2O8.

DOI： 10.1103/PhysRevLett.99.087602

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We report a study on the ground states of the triangular antiferromagnetic Ising model with a spacial anisotropy in the magnetic field. By the use of the level- spectroscopy and the density- matrix renormalization- group methods, we precisely determine the field- induced Berezinskii - Kosterlitz Thouless transition point and the Pokrovski - Talapov transition points with an anisotropic nature. Then we provide the global phase diagram of the present model.

DOI： 10.1088/0953-8984/19/14/145236

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Using numerical methods, we study the finite-field ground state of an S = 1 zigzag ladder. Special attention is paid to the magnetization plateau which appears at a half of the saturation magnetization in the ground-state magnetization curve. (c) 2006 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.jmmm.2006.10.316

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An S = (1)/(2) three-leg antiferromagnetic spin nanotube is investigated using the DMRG method and the level spectroscopy analysis combined with the numerical exact diagonalization. It is known that the system has a spin gap, when the three rung couplings are equivalent. In this paper, we see that as one of the three rung exchanges varies, a quantum phase transition occurs at a critical value of the varied rung exchange, and then the system is in a gapless Tomonaga-Luttinger-liquid phase. A ground-state phase diagram containing this phase transition is obtained by the phenomenological renormalization. (c) 2006 Published by Elsevier B.V.

DOI： 10.1016/j.jmmm.2006.10.431

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We investigate the filling dependence of the zigzag Hubbard ladder, which is a relevant model to the recently synthesized quasi-one-dimensional super conductor Pr2Ba4Cu7O15-delta(Pr247). Using the density matrix renormalization group method, we calculate chemical potential-electron density (mu-rho) curve of the model and then discuss the relation between the oxygen-deficiency and transition temperature in Pr247. (c) 2006 Published by Elsevier B.V.

DOI： 10.1016/j.jmmm.2006.10.300

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We study an incommensurate long-range order induced by an external magnetic field in a quasi-one-dimensional bond-alternating spin system, F5PNN, focusing on the role of the frustrating interaction which can be enhanced by a high-pressure effect. On the basis of the density matrix renormalization group analysis of a microscopic model for F5PNN, we present several H-T phase diagrams for typical parameters of the frustrating next-nearest-neighbour coupling and the interchain interaction, and then discuss how the field-induced incommensurate order develops by the frustration effect in such phase diagrams. A magnetization plateau at half the saturation moment is also mentioned.

DOI： 10.1088/0953-8984/18/20/006

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The field-induced Berezinskii-Kosterlitz-Thouless (BKT) transition in the ground state of the triangular antiferromagnetic Ising model is studied by the level-spectroscopy method. We analyze dimensions of operators around the BKT line, and estimate the BKT point H-c similar or equal to 0.5229 +/- 0.001, which is followed by the level-consistency check to demonstrate the accuracy of our estimate. Further we investigate the anisotropic case to clarify the stability of the field-induced string-density plateau against an incommensurate liquid state by the density-matrix renormalization-group method.

DOI： 10.1103/PhysRevE.73.035105

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We present a construction of a matrix product state (MPS) that approximates the largest-eigenvalue eigenvector of a transfer matrix T of a two-dimensional classical lattice model. A state vector created from the upper or the lower half of a finite size cluster approximates the largest-eigenvalue eigenvector. Decomposition of this state vector into the MPS gives a way of extending the MPS recursively. The extension process is a special case of the product wave function renormalization group (PWFRG) method, that accelerates the numerical calculation of the infinite system density matrix renormalization group (DMRG) method. As a result, we successfully give the physical interpretation of the PWFRG method, and obtain its appropriate initial condition. ©2006 The Physical Society of Japan.

DOI： 10.1143/JPSJ.75.014003

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We investigate the S=1 frustrated antiferromagnetic quantum spin chain in magnetic field, using numerical exact diagonalization of finite-size clusters. The calculated critical exponents of the spin correlation functions indicate that the incommensurate spin correlation parallel to the external field can be stronger than the transverse antiferromagnetic one for some intermediate fields. When such an incommensurate correlation is dominant, the quasi-1D system with finite interchain interactions should exhibit long-range incommensurate order. We also discuss a possible mechanism for the recently observed field-induced phase of NDMAP within this framework.

DOI： 10.1063/1.2355071

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We have performed high field magnetization measurements on the quasi one-dimensional (1D) antiferromagnet BaCo2V2O8, which shows a curious field-induced order-disorder transition, in pulsed magnetic fields up to 55 T. The observed magnetization curves up to the saturation field show non-linear increases, suggesting a strong quantum fluctuation. We analyze the magnetization curves in terms of the S = 1/2 1D XXZ model.

DOI： 10.1088/1/1742-6596/51/1/021

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Recently some quantum spin systems on tube lattices, so-called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As a first step of theoretical study oil the spin nanotube, we investigate the S = 1/2 three-leg spin tube, which is the simplest one, using numerical analyses of finite clusters and a finite-size scaling technique. The spin gap, which is one of the most interesting quantities reflecting the macroscopic quantum effect, was revealed to be open for ally finite rung exchange couplings, in contrast to the three-leg spin ladder system which is gapless. We also found a quantum phase transition caused by an asymmetric rung interaction. When one of the three rung coupling constants is changed, the spin gap vanishes very rapidly. (c) 2005 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.physe.2005.06.044

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We investigate, using numerical methods, the finite-field ground-state properties of an S = 1 anisotropic antiferromagnetic chain described by the Hamiltonian H=Sigma(l){S-l(x) S-l+1(x) + S-l(y) S-l+1(y) + Delta S-l(z) Sl+1} + d Sigma(l)(S-l(z)). It is found that the magnetization jump anomaly (a first-order phase transition) appears in the ground-state magnetization curve when Delta=5.0 and -1.50 less than or similar to D less than or similar to 1.05; in a certain region of D, the jump starts from a finite value of the magnetization m per spin. We also find that the a second-order phase transition between commensurate and incommensurate gapless phases takes place in the finite-field ground state. The critical point of this transition as well as the values of m at the onset and end of the magnetization jump is summarized in the m versus D phase diagram.

DOI： 10.1143/PTPS.159.77

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A mechanism of the magnetization plateau observed in the high-field magnetizatiom measurement of the organic S = 1 spin ladder system BIP-TENO is investigated. Assuming possible lattice distortion, we propose a possible scenario of the plateau formation on the basis of the bond-alternating ladder. Some unsolved problems are also discussed.

DOI： 10.1143/PTPS.159.251

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In this paper, we investigate the low-energy properties of the S = 1/2 anriferromagnetic quantum spin tube with the triangular lattice structure. Using the density matrix renormalization group (DMRG) method, we calculate the singlet-triplet excitation gap up to 144 triangles along the leg direction. Analyzing the size dependence of the gap, we find that the system is gapful for alpha &lt; 1.2. A similar analysis of the low-field edge of the magnetization curve suggests that the system is gapless for alpha &gt; 1.2.

DOI： 10.1143/PTPS.159.297

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We measured the magnetization processes of the S = 1/2 antiferromagnetic chain compound, Cu benzoate. From the inelastic neutron scattering and the specific heat measurements it was recently discovered that the substance exhibits an unexpected gap which varies approximately as the 2/3 power of an applied magnetic field. The primary mechanism of the gap formation is produced by an effective staggered field due to both the alternating g-tensor and the Dzyaloshinskii-Moriya interaction. We observed the effect of the effective staggered field on the magnetization process of Cu benzoate as a rounding behavior near the saturation field as well as an initial nonlinear increment near zero field. The experimental results are well reproduced by the numerical calculation on the Hamiltonian which includes the appropriate term of the staggered field, using the finite temperature density matrix renormalization group method.

DOI： 10.1143/PTPS.159.158

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The magnetization process of the S = 1 spin ladder system with bond-alternation due to the static lattice distortion is investigated by the numerical diagonalization of finite clusters and the level spectroscopy method. We focus our attention mainly on the magnetization plateau caused by field-induced spin gap. The plateau phase diagram is presented at M-s/4, where M-s is the saturated magnetization. In addition we discuss the magnetic curves and the mechanisms of the plateau at M-s/4 observed in the high field magnetization measurement of organic S = 1 ladder compound BIP-TENO.

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We investigate, at T = 0, the magnetization process of the S = 1 frustrated two-leg spin ladder having the leg interaction (J), the rung interaction (J(0)) and the diagonal interaction (J(d)), especially focusing on the appearance and the disappearance of the magnetization plateaux. We use the degenerate perturbation theory, the level spectroscopy analysis of the numerical diagonalization data and the DMRG. When J(d) = 0, the M-s/2 plateau (M-s is the saturation magnetization) appears for J(0)/J &gt; 1.463. Then there is no M-s/2 plateau for the so-called isotropic case J = J(0). In case of J(d) &gt; 0, J(d) helps the M-s/2 plateau. And also, the M-s/4 and (3/4) Ms plateaux appear when Jd is sufficiently large. These two plateaux are associated with the spontaneous breaking of the translation symmetry along the leg direction. We show the plateau phase diagram on the J(d) versus J plane, and also the magnetic phase diagram on the H versus J(d) plane for fixed J.

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We demonstrate that domain-wall type excitations carrying the fractional magnetization S-z = +/- 1/3 and their bound state describe the low-energy physics around the 1/3 plateau of the antiferromagnetic zigzag spin chain in the strongly frustrated region. In particular we discuss the relevance of such domain-wall excitations to the characteristic properties of the magnetization curves: the 1/3 plateau accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve.

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We study field-induced phase transitions and long-range orders in the S = 1/2 spin bond-alternating chain with frustrating interaction. By using the inter-chain mean field theory combined with the finite temperature density matrix renormalization group, we investigate properties of field-induced long-range orders and phase transitions. We find that the inter-chain interaction strongly affects the realized phases of this system.

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High-field magnetization and susceptibility measurements have been performed on S = 1 antiferromagnetic bond-alternating chain compounds: [Ni 2(dpt)2(μ-ox)(μ-N3)](PF6) [dpt=bis(3-aminopropyl)amine, ox= C2O4] (abbreviated as NDOAP) and [Ni(333-tet)(μ-tet)(μ-NO2)] ClO4 [333-tet=N,N′-bis(3-aminopropyl)-1,3-propanediamine] (abbreviated as NTENP). The magnetization of NDOAP shows two steep increases at about 200 and 500 kOe. A magnetization plateau is observed between about 300 and 500 kOe, corresponding to half the value of the saturation moment. Comparison between numerical calculations and the experimental results, including the magnetic susceptibility, shows that NDOAP has a singlet ground state due to dimerization with a bond-alternating ratio α=0.1. The half-saturation plateau is also observed around 700 kOe in the magnetization of NTENP. The magnetization process of NTENP is well reproduced by the numerical result calculated for the parameter of α=0.45 in the singlet-dimer phase. The a dependence of the magnetization processes is discussed.

DOI： 10.1103/PhysRevB.69.174405

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Recently, the organic compound biphenyl (BIP-TENO) was synthesized and found to be the first S = 1 spin ladder. The present high-field measurement up to 70 T indicates that a plateau appears in the magnetization curve at M = M(s)/4, where Ms is the saturation magnetization. We propose possible mechanisms of the M = M(s)/4 plateau in BIP-TENO. The frustration in the first, second and third neighbor antiferromagnetic exchange interactions in the S = 1 ladder yields the M = M(s)/4 plateau, with a spontaneous breaking of the translational symmetry. This can be known by use of the degenerate perturbation theory from the strong rung coupling limit. By use of the numerical diagonalization method, we revealed that the most realistic mechanism of the M = M(s)/4 plateau in BIP-TENO is due to the third neighbor interaction. Further theoretical analyses suggest the present mechanism should also lead to a cusp in the magnetization curve. The cusp-like anomaly in the experimental magnetization curve is a considerable evidence for our mechanism. We also discuss the M(s)/2 plateau problem. We show that a small rung coupling cannot yield the M(s)/2 plateau, which is quite different from the M = 0 plateau problem of the S = 1/2 ladder. 2 (C) 2004 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.physb.2004.01.015

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Using numerical methods, we study the finite-field ground state of an anisotropic S = 1/2 antiferromagnetic chain with bond-alternating nearest-neighbor and uniform next-nearest-neighbor interactions. Special attention is paid to the magnetization plateaux at a half and one-third of the saturation magnetization, which appear in the ground-state magnetization curve. (C) 2004 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.physb.2004.01.018

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We study, at T = 0, the anomalies in the magnetization curve of the S = 1 two-leg ladder with frustrated interactions. We focus mainly on the existence of the M = Ms/2 plateau, where Ms is the saturation magnetization. We report the results using the degenerate perturbation theory and the density matrix renormalization group, which lead to consistent conclusion with each other. We also touch on the M = Ms/4 and (3/4)Ms plateaux and cusps.

DOI： 10.1088/0953-8984/16/11/030

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The magnetization process of an Ising-type S = 1 spin chain with nearest-neighbour interaction (J(1)), next-nearest-neighbour interaction (J(2)) and single-ion anisotropy (D) is investigated on the basis of the ground state phase diagram of the chain in a magnetic field (H greater than or equal to 0). The 49 possible spin structures for the ground state are obtained using Morita's theorem. The magnetization process is obtained from the ground state phase diagram, giving J(2)/J(1) versus H/J(1), determined by comparing the energies of the 49 spin structures. It is shown that (1) among the 49 spin structures, 14 structures with unit cells of &lt;+&gt;, &lt;0&gt;, &lt;+-&gt;, &lt;+0&gt;, &lt;+ + -&gt;, &lt;+ + 0&gt;, &lt;+ - 0&gt;, &lt;+00&gt;, &lt;+ + - -&gt;, &lt;+ + 0-&gt;, &lt;+ + 00&gt;, &lt;+ + -0&gt;, &lt;+ - +00&gt; and &lt;+ + -0 + 0-&gt; appear in the phase diagram; (2) the magnetization process is equivalent to that of the usual Ising model for D less than or equal to 0; (3) a long period spin structure, &lt;+ + -0 + 0-&gt;, is realized for the intermediate ranges of J(2)/J(1) and D/J(1) due to the frustration of the system.

DOI： 10.1088/0953-8984/16/11/027

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We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag XXZ chain. We analyze the low-energy excitations around the plateau with the degenerating perturbation theory from the Ising limit, combined with the Bethe-form wave function. We then find that the domain-wall particles carrying S-z=+/-1/3 and its bound state of S-z=+/-2/3 describe well the low-energy excitations around the 1/3 plateau state. The formation of the bound state of the domain walls clearly provides the microscopic mechanism of the cusp singularities and the even-odd behavior in the magnetization curve.

DOI： 10.1103/PhysRevB.68.224422

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We study the magnetization process of a quasi-one-dimensional S=1 antiferromagnet with bond alternation by using the density matrix renormalization group method combined with interchain mean-field approximation. Particularly, we discuss how the interchain couplings affect the magnetization curve around a plateau structure in both of the Haldane phase and the dimer phase. It is shown that the antiferromagnetic correlation induced by the interchain couplings reduces the region of the plateau significantly, which will play an important role when the theoretical results are compared with actual measurements of the magnetization.

DOI： 10.1142/S021797920201436X

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

We investigate the magnetization process for a quasi-one-dimensional S=1 antiferromagnet with bond alternation. By combining the density matrix renormalization group method with the interchain mean-field theory, we discuss how the interchain coupling affects the magnetization curve. It is found that the width of the magnetization plateau is considerably reduced upon introducing the interchain coupling. We obtain the phase diagram in a magnetic field. The effect of single-ion anisotropy is also addressed.

DOI： 10.1103/PhysRevB.65.214405

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PERGAMON-ELSEVIER SCIENCE LTD  

We study the hole-doping effects on the frustrated orthogonal-dimer spin model with linked-tetrahedra chain structure. By using the density matrix renormalization group method we discuss how the metal-insulator transition is affected by geometrical frustration. When the system is in the dimer-singlet phase, hole-doping smoothly drives the system to a metallic phase. In contrast when the system is in the plaquette-singlet phase strong frustration induces the first-order transition to a metallic phase upon hole-doping which is characterized by the discontinuity in the electron density. We compute the spin correlation function to clarify the origin of the first-order phase transition. (C) 2002 Elsevier Science Ltd. All rights reserved.

DOI： 10.1016/S0022-3697(02)00106-3

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

We propose a matrix product state (MPS) formulation to calculate thermodynamic quantities of one dimensional (1D) quantum systems. The maximum-eigenvalue eigenstate of the quantum transfer matrix is represented as the product, of local matrices, which are obtained by the DMRG method for the two dimensional (2D) classical system mapped from the original ID quantum system. This MPS formulation is successfully applied to the S = 1/2 XY model.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

We give a short review of the cusp singularity in the magnetization curve of ID quantum spin systems. We show that the cusp singularity appears for a certain class of nonintegrable frustrated spin systems, using the density matrix renormaziation group method. We also discuss the cusp appearance mechanism on the basis of the one particle dispersion curve of the elementary excitation, where the shape change of the dispersion curve induced by the frustrated interaction plays an essential role.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

We give a short review of our recent works on the first-order quantum phase transitions in frustrated spin chains with orthogonal-dimer structure. When the ratio of the competing antiferromagnetic exchange couplings is varied, a first-order transition occurs between the dimer phase and the plaquette phase, which is accompanied by the discontinuity in the spin excitation gap. We further show that strong frustration triggers the phase transitions in a magnetic field, which exhibit plateaus and jumps in the magnetization curve. The hole-doping effect is also addressed for the orthogonal-dimer chain with linked-tetrahedra structure. It is found that the competing antiferromagnetic interactions result in a first-order metal-insulator transition upon hole doping.

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We investigate one-dimensional S = 1/2 and S = 1 antiferromagnetic quantum-spin chains with easy-axis anisotropies in a transverse field. We calculate both the uniform magnetization and the staggered magnetization, using a variant of the density-matrix renormalization-group method. We find that the staggered magnetizations exhibit reentrant behavior as functions of the transverse field, where the competition between the classical Néel order and the quantum fluctuations plays an important role. We also discuss the critical behavior associated with the staggered magnetizations.

DOI： 10.1103/PhysRevB.64.224422

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We investigate the low-lying excitation of the antiferromagnetic zigzag spin ladder with Mobius boundary condition. Using the Lanczos and Householder diagonalization methods, we calculate the excitation spectrum of the zigzag ladder in the momentum space. We then show that the topological defect generated by the Mobius boundary provides the clear evidence of the single-spinon excitation. On the basis of the obtained single-spinon dispersion curve, we analyze the two-spinon scattering states under the usual periodic boundary condition. We further discuss the interaction effect between the spinons, and the connection to the cusp singularity in the magnetization process.

DOI： 10.1103/PhysRevLett.87.212406

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We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the maximum-eigenvalue eigenstate of the transfer matrix as the product of local tensors that are iteratively optimized by the use of the "vertical density matrix" formed by cutting the system along the transfer direction. This algorithm, which we call vertical density matrix algorithm (VDMA), is successfully applied to the 3D Ising model. Using the Suzuki-Trotter transformation we can also apply the VDMA to 2D quantum systems, which we demonstrate for the 2D transverse field Ising model.

DOI： 10.1103/PhysRevE.64.016705

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The results of magnetic susceptibility and high held magnetization measurements on a single crystal sample of copper zigzag chain compound (N2H5)CuCl3 are reported. Magnetic susceptibility of this compound shows a round maximum around 10K and decreases gradually. High-field magnetization up to 300kOe of this compound shows a monotonic increase with a concave curvature. We compared the experimental results with those of calculation by the temperature-dependent density-matrix-renormalization-group method and obtained fairly good agreement between them when the ratio of the next-nearest-neighbor exchange constant to the nearest neighbor one is 0.2 similar to 0.3. (C) 2001 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0921-4526(00)00614-1

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We investigate the low-lying excitation of the antiferromagnetic zigzag spin ladder with Möbius boundary condition. Using the Lanczos and Householder diagonalization methods, we calculate the excitation spectrum of the zigzag ladder in the momentum space. We then show that the topological defect generated by the Möbius boundary provides the clear evidence of the single-spinon excitation. On the basis of the obtained single-spinon dispersion curve, we analyze the two-spinon scattering states under the usual periodic boundary condition. We further discuss the interaction effect between the spinons, and the connection to the cusp singularity in the magnetization process. © 2001 The American Physical Society.

DOI： 10.1103/PhysRevB.64.212406

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We investigate the low-energy properties of the orthogonal-dimer spin chain characterized by a frustrated dimer-plaquette structure. When the competing antiferromagnetic couplings are varied, the first-order quantum phase transition occurs between the dimer and the plaquette phases, which is accompanied by nontrivial features due to frustration. besides the discontinuity in the lowest excitation gap at the transition point, a sharp level crossing occurs for the spectrum in the plaquette phase. We further reveal that the plateau in the magnetization curve at 1/4 of the full moment dramatically changes its character in the vicinity of the critical point. It is argued that the first-order phase transition in this system captures some essential properties found in the two-dimensional orthogonal-dimer model proposed for SrCu2(BO3)(2).

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We study thermodynamic behaviors of the antiferromagnetic zigzag spill chain in magnetic fields, using the density-matrix renormalization-group method for the quantum transfer matrix. We focus on the thermodynamics of the system near the critical fields in the ground-state magnetization process (M-H curve): the saturation field, the lower critical field associated with excitation gap, and the field at the middle-field cusp singularity. We calculate magnetization. susceptibility, and specific heat of the zigzag chain in magnetic fields at finite temperatures. and then discuss how the calculated quantities reflect the low-lying excitations of the system related with the critical behaviors in the M-H curve.

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We study the zero-temperature magnetization process (M-H curve) of one-dimensional quantum antiferromagnets using a variant of the density-matrix renormalization group method. For both the S=1/2 zig-zag spin ladder and the S=1 bilinear-biquadratic chain, we find clear cusp-type singularities in the middle-field region of the M-H curve. These singularities are successfully explained in terms of the double-minimum shape of the energy dispersion of the low-lying excitations. For the S=1/2 zig-zag spin ladder, we find that the cusp formation accompanies the Fermi-liquid to non-Fermi-liquid transition. [S0163-1829(99)50834-5].

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We investigate magnetization process (M-H curve) of S = 1 bilinear-biquadratic (BLBQ) spin chain near critical fields at finite temperatures. We use the density matrix renormalization group (DMRG) for the two-dimensional classical lattice model mapped by the Trotter decomposition, with a help of the Baxter's variational principle. By comparing the DMRG result of S = 1/2 XY chain with the exact solution, we show that the DMRG is an efficient tool to calculate the M-H curve at finite temperatures. Further, we compute the M-H curve of the BLBQ chain. We compare the DMRG curve of the magnetization process of the BLBQ chain with those obtained by analytic approaches: correctly mapped delta-function. Bose-gas approach acid "Bethe-ansatz approximation" approach. Near the saturation field, we show that the delta-function Bose gas and the Bethe-ansatz approximation describe the M-H curve well in both at zero temperature and finite temperatures. Near the lower critical field, we find that the delta-function Bose gas. is a good effective model at the Heisenberg point. We further find that the delta-function Bose gas cannot describe the M-H curve at finite temperatures, near the special point where the M-H curve changes qualitatively. [S0163-1829(99)02730-7].

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We study the asymptotic behavior of the eigenvalue distribution of the corner transfer matrix (M-CTM) and the density matrix (M-DM) in the density-matrix renormalization group. We utilize the relationship MDM = M-CTM(4), which holds for noncritical systems in the thermodynamic limit. We derive the exact and universal asymptotic form of the hl,M-DM eigenvalue distribution for a class of integrable models in the massive regime. For nonintegrable models, the universal asymptotic form is also verified by numerical renormalization group calculations. [S1063-651X(99)50806-4].

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We study the zero-temperature magnetization curve (M-H curve) of the one-dimensional quantum anti-ferromagnet of spin one. The Hamiltonian H we consider is of the bilinear-biquadratic form: H = Sigma(i)f((s) over right arrow(i).s(i+1)) (+Zeeman term) where (s) over right arrow(i) is the spin operator at site i and f(X) = X + beta X-2 with 0 less than or equal to beta &lt; 1. We focus on validity of the delta-function Bose-gas picture near the two critical fields: upper-critical field H-s above which the magnetization saturates and the lower-critical field H-c associated with the Haldane gap. As for the behavior near H-s, we take ''low-energy effective S matrix" approach, where the correct effective Bose-gas coupling constant c is extracted from the two down-spin S matrix in its low-energy limit. We find that the resulting value of c differs from the spin-wave value. We draw the M-H curve by using the resultant Bose gas, and compare it with numerical calculation where the product-wave-function renormalization-group (PWFRG) method, a variant of White's density-matrix renormalization group method, is employed. Excellent agreement is seen between the PWFRG calculation and the correctly mapped Bose-gas calculation. We also test the validity of the Bose-gas picture near the lower-critical field H-c. Comparing the PWFRG-calculated M similar to H curves with the Bose-gas prediction, we find that there are two distinct regions, I and II, of beta separated by a critical value beta(c)(approximate to 0.41). In region I, 0 &lt; beta &lt; beta(c), the effective Bose coupling c is positive but rather small. The small value of c makes the "critical region" of the square-root behavior M similar to root H-H-c very narrow. Further, we find that in the beta --&gt; beta(c) - 0, the square-root behavior transmutes to a different one, M similar to (H - H-c)(theta) with theta approximate to 1/4. In region II, beta(c) &lt; beta &lt; 1, the square-root behavior is more pronounced as compared with region I, but the effective coupling c becomes negative. [S0163-1829(99)09009-8].

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Language：English   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

The density matrix renormalization group theory is reviewed as a numerical variational method. The variational state, expressed as a product of local tensors, is improved through locally tuning each tensor. The first section is a tutorial with simplified discussions. Details are discussed in the subsequent sections. The review concludes with some recent developments and future directions.

DOI： 10.1142/S0217979299000023

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：IOP PUBLISHING LTD  

We study the ground-state properties of two-dimensional quantum spin systems having the valence-bond-solid (VBS) type ground states. The 'product-of-tensors' form of the ground-state wavefunction of the system is utilized to associate it with an equivalent classical lattice statistical model which can be treated by the transfer-matrix method. For diagonalization of the transfer matrix, we employ the product-wavefunction renormalization group method, which is a variant of the density-matrix renormalization group method. We obtain the correlation length and the sublattice magnetization accurately. For the anisotropically 'deformed' S = 3/2 VBS model on the honeycomb lattice, we find that the correlation length as a function of the deformation parameter behaves very much as that in the S = 3/2 VBS chain.

DOI： 10.1088/1367-2630/1/1/007

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG BERLIN  

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The density matrix renormalization group is a variational approximation method that maximizes the partition function - or minimize the ground state energy - of quantum lattice systems. The variational relation is expressed as Z = Tr rho greater than or equal to Tr (&lt;(1) over tilde&gt;rho), where rho is the density submatrix of the system, and (1) over tilde is a projection operator. In this report we apply the variational relation to two-dimensional (2D) classical lattice models, where the density submatrix rho is obtained as a product of the corner transfer matrices. The obtained renormalization group method for 2D classical lattice model, the corner transfer matrix renormalization group method, is applied to the q = 2 similar to 5 Potts models. With the help of the finite size scaling, critical exponents (q = 2, 3) and the latent heat (q = 5) are precisely obtained.

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Language：English   Publisher：arXiv e-prints  

Motivated by sine-square deformation (SSD) for quantum critical systems in 1+1-dimension, we discuss a Mobius quantization approach to the two-dimensional conformal field theory (CFT), which bridges the conventional radial quantization and the dipolar quantization recently proposed by Ishibashi and Tada. We then find that the continuous Virasoro algebra of the dipolar quantization can be interpreted as a continuum limit of the Virasoro algebra for scaled generators in the SSD limit of the Mobius quantization approach. <P />...

DOI： 10.1093/ptep/ptw060

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DOI： 10.11316/jpsgaiyo.71.1.0_1336

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DOI： 10.11316/jpsgaiyo.71.2.0_2872

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Using Monte Carlo simulations, we explore the magnetic phase diagram of triangular spin tubes coupled with a ferromagnetic intertube interaction for CsCrF<SUB>4</SUB>. The planar structure of the coupled tubes is topologically equivalent to the kagome-triangular lattice, which induces nontrivial frustration effects in the system. We particularly find that, depending on the intertube coupling, various ordered phases are actually realized, such as incommensurate order, ferromagnetic order, and cuboc order, which is characterized by the noncoplanar spin structure of the 12 sublattices accompanying the spin chirality breaking. We also discuss the relevance of the results to recent experiments on CsCrF<SUB>4</SUB>. <P />...

DOI： 10.1103/PhysRevB.91.224403

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DOI： 10.11316/jpsgaiyo.70.1.0_2843

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We report magnetization, specific heat, and NMR measurements of 3-Br-4-F-V [=3-(3-bromo-4-fluorophenyl)-1,5-diphenylverdazyl], a strong-rung S =1/2 Heisenberg spin ladder with ferromagnetic leg interactions. We explain the magnetic and thermodynamic properties based on the strong-rung regime. Furthermore, we find a field-induced successive phase transition in the specific heat and the nuclear spin-lattice relaxation rate 1/T<SUB>1</SUB>. <SUP>19</SUP>F-NMR spectra for higher- and lower-temperature phases indicate partial magnetic order and incommensurate long-range order, respectively, evidencing the presence of frustration due to weak interladder couplings. <P />...

DOI： 10.1103/PhysRevB.89.220402

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Language：English   Publishing type：Internal/External technical report, pre-print, etc.   Publisher：AMER PHYSICAL SOC  

We discuss the topological disentangler for S = 1 quantum spin chains in the Haldane phase. We first point out that theKennedy-Tasaki (KT) nonlocal unitary transformation is the perfect disentangler for the Affleck-Kennedy-Lieb-Tasaki model. We then demonstrate that the KT transformation can be reconstructed as an assembly of pair disentanglers. Finally, we show that the KT transformation can be regarded as a topological disentangler, which selectively disentangles the twofold degeneracy in the entanglement spectrum of the S = 1 Heisenberg chain.

DOI： 10.1103/PhysRevB.83.104411

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From neutron diffraction measurements on a quasi-1D Ising-like Co2+ spin compound BaCo2V2O8, we observed an appearance of a novel type of incommensurate ordering in magnetic fields. This ordering is essentially different from the Neel-type ordering, which is expected for the classical system, and the peculiar spin structure is caused by quantum fluctuation inherent in the quantum spin chain. A Tomonaga-Luttinger liquid nature characteristic of the gapless quantum 1D system is responsible for the realization of the incommensurate ordering.

DOI： 10.1103/PhysRevLett.101.207201

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We calculate the vector spin chirality for S = 1/2 zigzag spin chains having U(l) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the zigzag XY chain and discuss the associated phase transition. The results are consistent with the analysis based on the bosonization and the long distance behaviour of the chirality correlation function. For the S = 1/2 zigzag Heisenberg chain in a magnetic field, we also verify the chiral order that is predicted by the effective field theory and the chirality correlation function, and then determine its magnetic phase diagram.

DOI： 10.1143/JPSJ.77.114004

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High-field specific heat measurements on BaCo2V2O8, which is a good realization of an S=1/2 quasi-one-dimensional (1D) Ising-like antifferomagnet, have been performed in magnetic fields up to 12 T along the chain and at temperature down to 200 mK. We have found a new magnetic ordered state in the field-induced phase above H-c similar or equal to 3.9 T. We suggest that a novel type of the incommensurate order, which is caused by the quantum effect inherent in the S = 1/2 quasi-1D Ising-like antiferromagnet, appears in the field-induced phase.

DOI： 10.1103/PhysRevLett.100.057202

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DOI： 10.11316/jpsgaiyo.63.1.3.0_497_4

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We present a novel real-space renormalization group (RG) for the one-dimensional XXZ model in the critical regime, reconsidering the role of the cutoff parameter in Wilson's RG for the Kondo impurity problem. We then demonstrate the RG calculation for the XXZ chain with the free boundary. Comparing the hierarchical structure of the obtained low-energy spectrum with the Bethe ansatz result, we find that the proper scaling dimension is reproduced as a fixed point of the RG transformation.

DOI： 10.1143/JPSJ.76.063001

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We investigate filling dependence of the zigzag Hubbard ladder using density-matrix renormalization group method. We illustrate the chemical-potential vs electron-density and spin gap vs electron-density curves, which reflect characteristic properties of the electron state. On the basis of the obtained phase diagram, we discuss the connection to a quasi-one-dimensional superconductor Pr2Ba4Cu7O15-delta.

DOI： 10.1103/PhysRevB.75.174514

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We present a real-space renormalization group approach for the corner Hamiltonian, which is relevant to the reduced density matrix in the density matrix renormalization group. A set of self-consistent equations that the renormalized Hamiltonian should satisfy in the thermodynamic limit is also derived from the fixed point of the recursion relation for the corner Hamiltonian. We demonstrate the renormalization group algorithm for the S = 1/2 XXZ spin chain and show that the results are consistent with the exact solution. We further examine the renormalization group for the S = 1 Heisenberg spin chain and then discuss the nature of the eigenvalue spectrum of the corner Hamiltonian for the nonintegrable model.

DOI： 10.1143/JPSJ.74.3186

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arXiv

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The frustration-induced enhancement of the incommensurate correlation for a bond-alternating spin chain in a magnetic field, associated with a quasi-one-dimensional organic compound F5PNN was studied. The temperature dependence of the staggered susceptibilities were investigated using the density matrix renormalization group. It was found that the incommensurate correlation becomes dominant in a certain range of the magnetic field. The mechanism of this enhancement were discussed on the basis of mapping to the effective S=1/2 XYZ chain and a possibility of the field-induced incommensurate long-range order.

DOI： 10.1103/PhysRevLett.93.127203

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We study the frustration-induced enhancement of the incommensurate correlation for a bond-alternating quantum spin chain in a magnetic field, which is associated with a quasi-one-dimensional organic compound F5PNN. We investigate the temperature dependence of the staggered susceptibilities by using the density matrix renormalization group, and then find that the incommensurate correlation becomes dominant in a certain range of the magnetic field. We also discuss the mechanism of this enhancement on the basis of the mapping to the effective S=1/2 XXZ chain and a possibility of the field-induced incommensurate long-range order.

DOI： 10.1103/PhysRevLett.93.127203

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The selection of the ground state among nearly degenerate states due to quantum fluctuations is studied for the S = 1/2 XY-like Heisenberg antiferromagnets on the triangular lattice in the magnetic field applied along the hard axis, which was first pointed out by Nikuni and Shiba. We find that the selected ground state sensitively depends on the degree of the anisotropy and the magnitude of the magnetic field. This dependence is similar to that in the corresponding classical model at finite temperatures where various types of field induced phases appear due to the entropy effect. It is also found that the similarities of the selected states in the classical and quantum models are not the case in a two-leg ladder lattice, although the lattice consists of triangles locally and the ground state of this lattice in the classical case is the same as that of the triangular lattice.

DOI： 10.1143/JPSJ.73.1798

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The selection of the ground state among nearly degenerate states due to quantum fluctuations is studied for the S = 1/2 XY-like Heisenberg antiferromagnets on the triangular lattice in the magnetic field applied along the hard axis, which was first pointed out by Nikuni and Shiba. We find that the selected ground state sensitively depends on the degree of the anisotropy and the magnitude of the magnetic field. This dependence is similar to that in the corresponding classical model at finite temperatures where various types of field induced phases appear due to the entropy effect. It is also found that the similarities of the selected states in the classical and quantum models are not the case in a two-leg ladder lattice, although the lattice consists of triangles locally and the ground state of this lattice in the classical case is the same as that of the triangular lattice.

DOI： 10.1143/JPSJ.73.1798

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High-field magnetization and susceptibility measurements have been performed on S=1 antiferromagnetic bond-alternating chain compounds: [Ni-2(dpt)(2)(mu-ox)(mu-N-3)](PF6) [dpt=bis(3-aminopropyl)amine, ox= C2O4] (abbreviated as NDOAP) and [Ni(333-tet)(mu-NO2)]ClO4 [333-tet=N,N-'-bis(3-aminopropyl)-1,3propanediamine] (abbreviated as NTENP). The magnetization of NDOAP shows two steep increases at about 200 and 500 kOe. A magnetization plateau is observed between about 300 and 500 kOe, corresponding to half the value of the saturation moment. Comparison between numerical calculations and the experimental results, including the magnetic susceptibility, shows that NDOAP has a singlet ground state due to dimerization with a bond-alternating ratio alpha=0.1. The half-saturation plateau is also observed around 700 kOe in the magnetization of NTENP. The magnetization process of NTENP is well reproduced by the numerical result calculated for the parameter of alpha=0.45 in the singlet-dimer phase. The alpha dependence of the magnetization processes is discussed.

DOI： 10.1103/PhysRevB.69.174405

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High-field magnetization and susceptibility measurements have been performed on S=1 antiferromagnetic bond-alternating chain compounds: [Ni-2(dpt)(2)(mu-ox)(mu-N-3)](PF6) [dpt=bis(3-aminopropyl)amine, ox= C2O4] (abbreviated as NDOAP) and [Ni(333-tet)(mu-NO2)]ClO4 [333-tet=N,N-'-bis(3-aminopropyl)-1,3propanediamine] (abbreviated as NTENP). The magnetization of NDOAP shows two steep increases at about 200 and 500 kOe. A magnetization plateau is observed between about 300 and 500 kOe, corresponding to half the value of the saturation moment. Comparison between numerical calculations and the experimental results, including the magnetic susceptibility, shows that NDOAP has a singlet ground state due to dimerization with a bond-alternating ratio alpha=0.1. The half-saturation plateau is also observed around 700 kOe in the magnetization of NTENP. The magnetization process of NTENP is well reproduced by the numerical result calculated for the parameter of alpha=0.45 in the singlet-dimer phase. The alpha dependence of the magnetization processes is discussed.

DOI： 10.1103/PhysRevB.69.174405

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The low-energy effective Hamiltonian is derived for a typical quasi-one-dimensional Ising-like antiferromagnet CsCoCl3. In contrast to previous treatments, in which only the processes within the crystal-field ground Kramers doublet are considered, second-order processes via crystal-field excited states are also taken into account in the present paper. They result in a new term, which is essentially a next-nearest neighbor ferromagnetic exchange whose anisotropy is different from the nearest-neighbor exchange. By including the new term the magnetization curve and ESR in CsCoCl3 are analyzed to show that those experiments can be explained in a way consistent with other experiments. Related theories on CsCoCl3 are discussed in this connection.

DOI： 10.1143/JPSJ.72.2326

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The low-energy effective Hamiltonian is derived for a typical quasi-one-dimensional Ising-like antiferromagnet CsCoCl3. In contrast to previous treatments, in which only the processes within the crystal-field ground Kramers doublet are considered, second-order processes via crystal-field excited states are also taken into account in the present paper. They result in a new term, which is essentially a next-nearest neighbor ferromagnetic exchange whose anisotropy is different from the nearest-neighbor exchange. By including the new term the magnetization curve and ESR in CsCoCl3 are analyzed to show that those experiments can be explained in a way consistent with other experiments. Related theories on CsCoCl3 are discussed in this connection.

DOI： 10.1143/JPSJ.72.2326

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The low-energy effective Hamiltonian is derived for a typical quasi-one-dimensional Ising-like antiferromagnet CsCoCl3. In contrast to previous treatments, in which only the processes within the crystal-field ground Kramers doublet are considered, second-order processes via crystal-field excited states are also taken into account in the present paper. They result in a new term, which is essentially a next-nearest neighbor ferromagnetic exchange whose anisotropy is different from the nearest-neighbor exchange. By including the new term the magnetization curve and ESR in CsCoCl3 are analyzed to show that those experiments can be explained in a way consistent with other experiments. Related theories on CsCoCl3 are discussed in this connection.

DOI： 10.1143/JPSJ.72.2326

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We present a theoretical and experimental study of a quasi-one-dimensional zigzag antiferromagnet (N2H5)CuCl3, which can be viewed as weakly coupled Heisenberg chains with a frustrated interaction. We first discuss generic features of the magnetic properties of the zigzag spin chain between the nearly single chain case and the nearly double chain case, on the basis of the finite temperature density-matrix renormalization group (DMRG) calculations. We next show the experimental results for the magnetic susceptibility and the high-field magnetization of a single crystal of (N2H5)CuCl3 above the Neel temperature T-N = 1.55 K. By comparing the experimental data with the DMRG results carefully, we finally obtain the ratio of the nearest and next-nearest exchange couplings as J(1)/J(2) = 0.25 with J(2)/k(B) = 16.3 K. We also investigate the three-dimensional (3D) coupling J' effect by using mean-field theory combined with the DMRG calculations. The estimated value J' similar to 0.04J(2) supports the one-dimensionality of (N2H5)CuCl3 above T-N.

DOI： 10.1088/0953-8984/15/21/309

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Hole-doping effects are investigated on the t-J ladder model with the linked-tetrahedra structure. We discuss how a metal-insulator transition occurs upon hole doping with particular emphasis on the effects of geometrical frustration. By computing the electron density and the spin correlation function by the density matrix renormalization group, we show that strong frustration triggers a first-order transition to a metallic phase, when holes are doped into the plaquette-singlet phase. By examining spin excitations in a metallic case in detail, we discuss whether the spin-gap phase persists upon hole doping according to the strength of frustration. It is further shown that the lowest excited state in a spin-gap metallic phase can be described in two independent quasiparticles.

DOI： 10.1143/JPSJ.72.405

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Hole-doping effects are investigated on the t-J ladder model with the linked-tetrahedra structure. We discuss how a metal-insulator transition occurs upon hole doping with particular emphasis on the effects of geometrical frustration. By computing the electron density and the spin correlation function by the density matrix renormalization group, we show that strong frustration triggers a first-order transition to a metallic phase, when holes are doped into the plaquette-singlet phase. By examining spin excitations in a metallic case in detail, we discuss whether the spin-gap phase persists upon hole doping according to the strength of frustration. It is further shown that the lowest excited state in a spin-gap metallic phase can be described in two independent quasiparticles.

DOI： 10.1143/JPSJ.72.405

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DOI： 10.1143/JPSJ.72.479

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We determine the magnetic phase diagram of the $S=1/2$ antiferromagnetic zigzag spin chain in the strongly frustrated region, using the density matrix renormalization group method. We find the magnetization plateau at $1/3$ of the full moment accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even–odd effect in the magnetization curve. We also discuss the formation mechanisms of the plateau and cusps briefly.

DOI： 10.1143/JPSJ.72.479

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We investigate the magnetization process for a quasi-one-dimensional S=1 antiferromagnet with bond alternation. By combining the density matrix renormalization group method with the interchain mean-field theory, we discuss how the interchain coupling affects the magnetization curve. It is found that the width of the magnetization plateau is considerably reduced upon introducing the interchain coupling. We obtain the phase diagram in a magnetic field. The effect of single-ion anisotropy is also addressed.

DOI： 10.1103/PhysRevB.65.214405

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We investigate one-dimensional S = 1/2 and S=1 antiferromagnetic quantum-spin chains with easy-axis anisotropies in a transverse field. We calculate both the uniform magnetization and the staggered magnetization, using a variant of the density-matrix renormalization-group method. We find that the staggered magnetizations exhibit reentrant behavior as functions of the transverse field, where the competition between the classical Neel order and the quantum fluctuations plays an important role. We also discuss the critical behavior associated with the staggered magnetizations.

DOI： 10.1103/PhysRevB.64.224422

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We investigate one-dimensional S = 1/2 and S=1 antiferromagnetic quantum-spin chains with easy-axis anisotropies in a transverse field. We calculate both the uniform magnetization and the staggered magnetization, using a variant of the density-matrix renormalization-group method. We find that the staggered magnetizations exhibit reentrant behavior as functions of the transverse field, where the competition between the classical Neel order and the quantum fluctuations plays an important role. We also discuss the critical behavior associated with the staggered magnetizations.

DOI： 10.1103/PhysRevB.64.224422

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We investigate the low-lying excitation of the antiferromagnetic zigzag spin ladder with Mobius boundary condition. Using the Lanczos and Householder diagonalization methods, we calculate the excitation spectrum of the zigzag ladder in the momentum space. We then show that the topological defect generated by the Mobius boundary provides the clear evidence of the single-spinon excitation. On the basis of the obtained single-spinon dispersion curve, we analyze the two-spinon scattering states under the usual periodic boundary condition. We further discuss the interaction effect between the spinons, and the connection to the cusp singularity in the magnetization process.

DOI： 10.1103/PhysRevLett.87.212406

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We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the maximum-eigenvalue eigenstate of the transfer matrix as the product of local tensors that are iteratively optimized by the use of the "vertical density matrix" formed by cutting the system along the transfer direction. This algorithm, which we call vertical density matrix algorithm (VDMA), is successfully applied to the 3D Ising model. Using the Suzuki-Trotter transformation we can also apply the VDMA to 2D quantum systems, which we demonstrate for the 2D transverse field Ising model.

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We present a new algorithm to calculate the thermodynamic quantities of three-dimensional (3D) classical statistical systems, based on the ideas of the tensor product state and the density matrix renormalization group. We represent the maximum-eigenvalue eigenstate of the transfer matrix as the product of local tensors that are iteratively optimized by the use of the "vertical density matrix" formed by cutting the system along the transfer direction. This algorithm, which we call vertical density matrix algorithm (VDMA), is successfully applied to the 3D Ising model. Using the Suzuki-Trotter transformation we can also apply the VDMA to 2D quantum systems, which we demonstrate for the 2D transverse field Ising model.

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We propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as a two-dimensional product of tensors. The variational partition function is calculated using the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The numerical efficiency of the method is exemplified in its application to the 3D Ising model.

DOI： 10.1143/PTP.105.409

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We discuss a universal relation (formula presented) with (formula presented) in 1D quantum spin systems with an excitation gap, where (formula presented) is the dispersion curve of the low-energy excitation and (formula presented) is the correlation length of the ground state. We first discuss this relation for integrable models such as the Ising model in a transverse filed and the (formula presented) model. We secondly make a derivation of the relation for general cases, in connection with the equilibrium crystal shape in the corresponding 2D classical system. We finally verify the relation for the (formula presented) bilinear-biquadratic spin chain and the (formula presented) zigzag spin ladder numerically. © 2001 The American Physical Society.

DOI： 10.1103/PhysRevB.64.104432

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DOI： 10.11316/butsuri1946.55.763

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We investigate the low-energy properties of the orthogonal-dimer spin chain characterized by a frustrated dimer-plaquette structure. When the competing antiferromagnetic couplings are varied, the first-order quantum phase transition occurs between the dimer and the plaquette phases, which is accompanied by nontrivial features due to frustration: besides the discontinuity in the lowest excitation gap at the transition point, a sharp level crossing occurs for the spectrum in the plaquette phase. We further reveal that the plateau in the magnetization curve at 1/4 of the full moment dramatically changes its character in the vicinity of the critical point. It is argued that the first-order phase transition in this system captures some essential properties found in the two-dimensional orthogonal-dimer model proposed for SrCu<SUB>2</SUB>(BO<SUB>3</SUB>)<SUB>2</SUB>. <P />...

DOI： 10.1103/PhysRevB.62.5558

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We study thermodynamic behaviors of the antiferromagnetic zigzag spin chain in magnetic fields, using the density-matrix renormalization-group method for the quantum transfer matrix. We focus on the thermodynamics of the system near the critical fields in the ground-state magnetization process (M-H curve): the saturation field, the lower critical field associated with excitation gap, and the field at the middle-field cusp singularity. We calculate magnetization, susceptibility, and specific heat of the zigzag chain in magnetic fields at finite temperatures, and then discuss how the calculated quantities reflect the low-lying excitations of the system related with the critical behaviors in the M-H curve. <P />...

DOI： 10.1103/PhysRevB.62.934

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Language：English   Publisher：ELSEVIER SCIENCE BV  

We propose a numerical variational method for three-dimensional (3D) classical lattice models. We construct the variational state as a product of local tensors, and improve it by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG) applied to 2D classical systems. Numerical efficiency of this approximation is investigated through trial applications to the 3D Ising model and the 3D 3-state Potts model. (C) 2000 Elsevier Science B.V. All rights reserved.

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We propose a numerical variational method for three-dimensional (3D)<br />
classical lattice models. We construct the variational state as a product of<br />
local tensors, and improve it by use of the corner transfer matrix<br />
renormalization group (CTMRG), which is a variant of the density matrix<br />
renormalization group (DMRG) applied to 2D classical systems. Numerical<br />
efficiency of this approximation is investigated through trial applications to<br />
the 3D Ising model and the 3D 3-state Potts model.

DOI： 10.1016/S0550-3213(00)00133-4

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We investigate the Kramers-Wannier approximation for the three-dimensional (3D) Ising model. The variational state is represented by an effective 2D Ising model, which contains two variational parameters. We numerically calculate the variational partition function using the corner transfer matrix renormalization group (CTMRG) method, and find its maximum with respect to the variational parameters. The value of the calculated transition point, K-c = 0.2184, is only 1.5% less than the true K-c. This result is better than that obtained using the corner transfer tensor renormalization group (CTTRG) approach. The calculated phase transition is mean-held like.

DOI： 10.1143/PTP.103.541

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