坂井 徹

We investigate the ground-state phase diagram of the bond-alternating S = 2 quantum spin chain with the XXZ and on-site anisotropies. For the on-site anisotropies, in addition to the popular D-2 Sigma(j)(S-j(z))(2) term, we consider the D-4 Sigma(j)(S-j(z))(4) term. Mainly we use the exact diagonalization and the level spectroscopy analysis. We show that the Haldane state, large-D state and the Dimer2 state belong to the same trivial phase, by finding the existence of adiabatic paths directly connecting these states without the quantum phase transition. Similarly, we show that the intermediate-D state and the Dimer1 state belong to the same symmetry protected topological phase.

We study the magnetization process of the spin-1/2 Heisenberg antiferromagnet on a distorted square-kagome lattice by the numerical-diagonalization method. The magnetization jump at one-third of the height of the saturation is examined in detail; we find that the jump becomes larger when a small distortion is switched on and that it is accompanied by an abrupt change in lines along microscopic spin directions. Our finite-size results successfully confirm that the magnetization jump in a spin-isotropic system is a macroscopic jump that survives in the thermodynamic limit and that the changes in spin directions are common to a spin-flop phenomenon observed in spin-anisotropic systems.

The S = 1/2 three-leg spin nanotube with the ring exchange interaction at each plaquette is investigated using the numerical diagonalization of finite-size systems. The previous work suggested that the system without the ring exchange interaction has a spin excitation gap between the singlet ground state and the triplet excitation, because a spontaneous dimerization occurs in the ground state. The present study indicates that as the ring exchange increases, a quantum phase transition occurs at some critical value to another spin gap phase where the pattern of the dimerization is different from the initial one. The spin gap is revealed to vanish at the phase boundary. The ground state phase diagram is also presented. (C) 2015 Elsevier B.V. All rights reserved.

The evolution of the filamentary 3-Kelvin (3-K) superconducting phase at the interface between Sr2RuO4 and Ru-metal inclusions is discussed for Pb-Ru-Sr2RuO4 contacts. Using the Ginzburg-Landau model, the influence of proximity-induced superconductivity in Ru on the topology of the 3-K phase is analyzed. Because the s-wave order parameter in Ru favors a 3-K state of trivial topology, the onset temperature of the phase with a nontrivial topology, which is compatible with the bulk phase of Sr2RuO4, is essentially reduced to the bulk transition temperature. Because the topology of the superconducting state in Sr2RuO4 is crucial for the Josephson effect through Pb-Ru-Sr2RuO4 contacts, this model qualitatively reproduces the experimental observation of the anomalous temperature dependence on the critical current.

The S = 1/2 kagome-lattice antiferromagnet is investigated by the numerical diagonalization of 18-spin finite-size cluster. The matrix elements proportional to the intensity of the singlet--triplet electron spin resonance (ESR) transition are calculated in the presence of the Dzyaloshinsky--Moriya interaction. Some angle-dependent selection rules are also proposed. The present result would be useful to examine whether the kagome-lattice antiferromagnet has a spin gap or not, with the ESR experiment.

The magnetization process of the spin-S Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. Our numerical-diagonalization data for small finite-size clusters with S = 1, 3/2, 2, and 5/2 suggest that a magnetization plateau appears at one-third of the height of the saturation in the magnetization process irrespective of S. We discuss the S dependences of the edge fields and the width of the plateau in comparison with recent results obtained by real-space perturbation theory.

To clarify the instability of the ferrimagnetism which is the fundamental magnetism of ferrite, numerical-diagonalization study is carried out for the two-dimensional S = 1/2 Heisenberg antiferromagnet with frustration. We find that the ferrimagnetic ground state has the spontaneous magnetization in small frustration; due to a frustrating interaction above a specific strength, the spontaneous magnetization discontinuously vanishes so that the ferrimagnetic state appears only under some magnetic fields. We also find that, when the interaction is increased further, the ferrimagnetism disappears even under magnetic field. (C) 2015 The Japan Society of Applied Physics

The magnetization process of the S = 1/2 Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. We successfully obtain a new result of the magnetization process of a 42-site cluster in the entire range. Our analysis clarifies that the critical behavior around one-third of the height of the saturation is different from the typical behavior of the well-known magnetization plateau in two-dimensional systems. We also examine the effect of the root 3 x root 3-type distortion added to the kagome lattice. We find at one-third of the height of the saturation in the magnetization process that the undistorted kagome point is just the boundary between two phases that show their own properties that are different from each other. Our results suggest a relationship between the anomalous critical behavior at the undistorted point and the fact that the undistorted point is the boundary.

Motivated by a recent finding of a spin-flop phenomenon in a system without anisotropy in spin space reported in the S = 1/2 Heisenberg antiferromagnet on the square-kagome lattice, we study the S = 1/2 Heisenberg antiferromagnets on two other lattices composed of vertex-sharing triangles by the numerical diagonalization method. One is a novel lattice including a shuriken shape with four teeth; the other is the kagome lattice with root 3 x root 3-structure distortion, which includes a shuriken shape with six teeth. We find in the magnetization processes of these systems that a magnetization jump accompanied by a spin-flop phenomenon occurs at the higher-field-side edge of the magnetization plateau at one-third the height of saturation. This finding indicates that the spin-flop phenomenon found in the isotropic system on the square-kagome lattice is not an exceptional case.

The magnetic phase diagram under a magnetic field of the spin-1/2 Heisenberg antiferromagnet on the Cairo pentagon lattice has been derived from a magnetization process and correlation functions calculated by numerical diagonalization for small clusters with up to 36 sites. The phase transition between two types of 1/3 magnetization states takes place, which continues to the orthogonal dimer state and ferrimagnetic state in the limits of x = 0 and x = infinity, respectively, where x is the ratio between two types of nearest-neighbor exchange interactions, in the absence of a magnetic field. A peculiar magnetization jump has been found at the lower- or higher-field edge of the 1/3 plateau, when x is larger or smaller than its critical value of similar to 0.8, respectively. The temperature dependence of the specific heat shows a double-peak structure.

We study the S = 1/2 Heisenberg antiferromagnet on the Cairo pentagon lattice by the numerical-diagonalization method. We tune the ratio of two antiferromagnetic interactions coming from two kinds of inequivalent sites in this lattice, examining the magnetization process of the antiferromagnet; particular attention is given to one-third of the height of the saturation. We find that quantum phase transition occurs at a specific ratio and that a magnetization plateau appears in the vicinity of the transition. The plateau is accompanied by a magnetization jump on one side among the edges due to the spin-flop phenomenon. Which side the jump appears depends on the ratio.

Experimental quest for the hypothetical " quantum spin liquid" state has recently met a few promising candidate materials including organic salts kappa-(ET)(2)Cu-2(CN)(3) and EtMe3Sb[Pd(dmit)(2)](2), S = 1/2 triangular-lattice Heisenberg antiferromagnets consisting of molecular dimers. These compounds exhibit no magnetic ordering nor the spin freezing down to very low temperature, while various physical quantities exhibit gapless behaviors. Recent dielectric measurements revealed the glassy dielectric response suggesting the random freezing of the electric polarization degrees of freedom. Inspired by this observation, we propose as a minimal model of the observed quantum spin-liquid behavior the S = 1/2 antiferromagnetic Heisenberg on the triangular lattice with a quenched randomness in the exchange interaction. We study both zero-and finite-temperature properties of the model by an exact diagonalization method, to find that when the randomness exceeds a critical value the model exhibits a quantum spin-liquid ground state. This randomness-induced quantum spin-liquid state exhibits gapless behaviors including the temperature-linear specific heat. The results provide a consistent explanation of the recent experimental observations on organic salts.

The S = 1/2 kagomelattice antiferromagnet is investigated by the numerical diagonalization. We successfully obtained the ground-state full magnetization curve for the 42-spin cluster. Based on the finite-size scaling alnalysis including this new result, we consider the quatnum critical magnetization behavior around the 1/3 of the saturation magnetization. As a result, some unconventional features of the 1/3 magnetization ramp, which was proposed by our previous work, are clarified.

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.

We investigate the ground-state phase diagram and critical properties of the S = 1/2 two-leg Heisenberg spin ladder system with a negative four-spin interaction using a numerical exact diagonalization method. Using the perturbation theory in the strong negative rung-coupling limit, we derive an S = 1 bilinear-biquadratic chain as an effective model. We discuss the ground-state phase diagram in this limit. Next we numerically determine a phase boundary between the rung singlet phase and the columnar dimer (CD) phase by the phenomenological renormalization group method, and one between the CD phase and the Haldane phase by the twisted boundary condition method. We confirm that the phase transition between the CD phase and the Haldane phase is of second order and this universality class is described by the k = 2 SU(2) Wess-Zumino-Novikov-Witten nonlinear sigma model, calculating the central charge and scaling dimensions.

The magnetization process of the S = 1/2 kagome-lattice quantum antiferromagnet is investigated using the numerical exact diagonalization up to 36-site clusters. Our previous finite-size scaling analysis with rhombic clusters indicated the "magnetization ramp" as a novel field-induced quantum phase transition at 1/3 the saturation magnetization. As another possible exotic behavior, we focus on the feature of the magnetization curve at 2/3 the saturation. The critical exponent analysis indicates that a different singular behavior occurs at the 2/3 magnetization.

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.

Using the numerical diagonalization method, we study the S = 1/2 Heisenberg antiferromagnet on a two-dimensional lattice composed of vertex-sharing triangles that we call the shuriken lattice. This lattice is similar to the kagome lattice but with a slight difference. We examine the ground-state properties and magnetization process of this model. We find that a magnetization jump appears at the higher-field-side edge of the magnetization plateau at one-third the height of saturation. A spin-flop phenomenon is clearly observed at the jump even when the system is isotropic in the spin space.

We study the S = 1 Heisenberg antiferromagnet on a spatially anisotropic triangular lattice by the numerical diagonalization method. We examine the stability of the long-range order of a three-sublattice structure observed in the isotropic system between the isotropic case and the case of isolated one-dimensional chains. It is found that the long-range-ordered ground state with this structure exists in the range of 0.7 less than or similar to J(2)/J(1) <= 1, where J(1) is the interaction amplitude along the chains and J(2) is the amplitude of other interactions.

The magnetization process of the S=1/2 Kagome-lattice quantum antiferromagnet is investigated using the numerical exact diagonalization up to 39-site clusters, comparing with the triangular-lattice antiferromagnet. Our previous finite-size scaling analysis with the rhombic clusters indicated the "magnetization ramp" as a novel field-induced quantum phase transition at 1/3 of the saturation magnetization. As another possible exotic behavior, we focus on the feature of the magnetization curve at the 2/3 of the saturation. The same critical exponent analysis indicates that a different singular behavior occurs at the 2/3 magnetization of the Kagome-lattice antiferromagnet, while no anomaly in the triangular-lattice one.

Using mainly numerical methods, we investigate the width of the spin gap of a spin-1/2 two-leg ladder described by ${\cal H} = J_{ { \rm l } } \sum\nolimits_{j = 1}<^>{N/2} {} [{\bf S}_{j,a} \cdot {\bf S}_{j + 1,a} + {\bf S}_{j,b} \cdot {\bf S}_{j + 1,b} ] + J_{ { \rm r } } \sum\nolimits_{j = 1}<^>{N/2} {} [\lambda (S_{j,a}<^>{x} S_{j,b}<^>{x} + S_{j,a}<^>{y} S_{j,b}<^>{y} ) + S_{j,a}<^>{z} S_{j,b}<^>{z} ]$, where $S_{j,a(b)}<^>{\alpha } $ denotes the -component of the spin-1/2 operator at the j-th site of the a (b) chain. We mainly focus on the $J_{ { \rm r } }$ >> $J_{ { \rm l } } > 0$ and $|\lambda |\ll 1$ case. The width of the spin gap between the M=0 and 1 subspaces (M is the total magnetization) as a function of anomalously increases near =0; for instance, for $- 0.1 $ less than or similar to $\lambda$ less than or similar to $0.1$ when Jl/Jr=0.1. The gap formation mechanism is thought to be different for the <0 and >0 cases. Since, in usual cases, the width of the gap becomes zero or small at the point where the gap formation mechanism changes, the above gap-increasing phenomenon in the present case is anomalous. We explain the origin of this anomalous phenomenon by use of the degenerate perturbation theory. We also draw the ground-state phase diagram.

Our previous numerical diagonalization study on the magnetization processes of the kagome- and triangular-lattice antiferromagnets revealed that the former system exhibits a new field-induced phenomenon, called a magnetization ramp, at 1/3 of the saturation magnetization, while the latter one a conventional magnetization plateau. To clarify the difference between the magnetization ramp and plateau, we consider a generalized lattice model with two exchange interactions J1 and J2, which corresponds to the kagome lattice for J2=0 and triangular one for J2=J1. The present numerical diagonalization study revealed that a quantum phase transition between the magnetization ramp and plateau occurs about J2/J1 approximate to 0.1.

High-field electron spin resonance (ESR) measurements of Bi3Mn4O12(NO3), which has been suggested recently as a new honeycomb lattice antiferromagnet with spin frustration, have been performed in a field region up to 20 T. An ESR measurement at 265 K shows an isotropic broad resonance, and the obtained g value is 1.974 +/- 0.016, which is consistent with the Mn4+ ion in a crystal field with low symmetry. At 1.8 K, resonances, whose frequency-field relation corresponds to antiferromagnetic resonance (AFMR) with an easy-plane type anisotropy and a Dzyaloshinsky-Moriya (DM) interaction, appear above 6 T. This result is consistent with the field-induced magnetic order (FIMO) phase suggested by a previous neutron measurement. From the analysis of our AFMR result, the D term of the DM interaction is estimated as 1.3 K, and the direction of the D term is suggested to be along the c axis, which is consistent with the crystal symmetry. Using this D and the exchange interaction, the canted angle is estimated to be 2.42 degrees, which can interpret the magnetization jump at the metamagnetic transition qualitatively. The possible origin of the FIMO phase is discussed with recent theoretical results within the J(1)-J(2) model.

A consistent description of the behaviors of both the magnetic susceptibility and of the 1/3-plateau like magnetization under a magnetic field in the triangulated-kagome compound Cu 9X 2(cpa) 6·nH 2O (X = F, Cl, Br; cpa = the anion of 2-carboxypentonic acid) is given by the Heisenberg model with the antiferromagnetic next-nearestneighbor interaction, in addition to the two types of antiferromagnetic nearest-neighbor interactions in previous studies. This description is provided by the method of numerical diagonalization. The newly introduced interaction derives the quantum phase transition from the quantum-disordered-state to the ferrimagnetic one. The stability of the magnetization plateaus is complemented using the perturbation theory. © 2012 The Physical Society of Japan.

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.

The magnetization process of the S = 1/2 kagome-lattice quantum antiferromagnet is investigated using the numerical exact diagonalization up to 39-site clusters. The finite-size scaling analysis with the rohmbic clusters indicated the "magnetization ramp" as a novel field-induced quantum phase transition at 1/3 of the saturation magnetization. The magnetization ramp is characterized by the following properties; (i) the field derivative dm/dH is divergent at the lower-field side, (ii) dm/dH is vanishing at the higher-field side, and (iii) there is a single critical field H-c (no plateau). Applying the critical exponent analysis for the non-rohmbic clusters, as well as the rohmbic ones, we confirmed the above properties of the magnetization at 1/3 of the saturation for the kagome lattice antiferromagnet.

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.

The spin nanotube has attracted a lot of interest as an intersection between the strongly correlated electronics and the nanoscience. Among spin nanotubes we focus on the S=1/2 three-leg spin tube, because it has the largest quantum fluctuation and the strongest frustration. Using the numerical exact diagonalization of the finite-cluster Heisenberg model, we reveal that two singlet ground states are degenerated in the spin gap phase of the spin tube. It is also found that the spin gap is characterized by the quantized Berry phase.

The specific heat and magnetic susceptibility of a spin-1/2 Ising-like anisotropic Heisenberg model (IAHM) on a kagome lattice are investigated by an exact diagonalization method for small clusters up to 18 spins with periodic boundary conditions. The enhancement of magnetic susceptibility from the Curie-Weiss law and the peak structure of specific heat at intermediate temperatures are attributed to a longitudinal (classical) spin fluctuation, and the steep decrease and the second peak at lower temperatures in those respective quantities to a transverse (quantum) spin fluctuation. It is verified that such anomalies may be produced by interruption by a semiclassical liquidlike state consisting of doubletlike triangular trimmers between a higher-temperature classical spin gaslike state and a lower-temperature quantum spin singlet state. The IAHM may give a general viewpoint for interpreting the experimentally observed thermodynamic properties of spin systems with various triangle-based lattices.

We study the system size dependence of the singlet-triplet excitation gap in the S = 1/2 kagome-lattice Heisenberg antiferromagnet by numerical diagonalization. We successfully obtain a new result of a cluster of 42 sites. The two sequences of gaps of systems with even-number sites and that with odd-number sites are separately analyzed. Careful examination clarifies that there is no contradiction when we consider the system to be gapless.

Thermodynamic properties, specific heat and magnetic susceptibility, of spin-1/2 Ising-like Heisenberg model are investigated by an exact diagonalization method for small finite size kagome- and triangular-lattices up to 18-spins. The enhancement of magnetic susceptibility from the Curie Weiss law and the peaks-structure of specific heat, rather generally detected experimentally in triangle-based spin systems including herbertsmithite, are interpreted as an intrinsic property of triangle-based frustrated spin systems with some extent of exchange anisotropy and are inferred as owing to a quantum-class crossover.

Using mainly numerical methods, we investigate the ground-state phase diagram of the S 2 quantum spin chain described by H = Sigma(j)((SjSj+1x)-S-x + (SjSj+1y)-S-y + Delta(SjSj+1z)-S-z) + D Sigma(j)(S-j(z))(2), where Delta denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and D the on-site anisotropy parameter. We restrict ourselves to the case of Delta >= 0 and D >= 0 for simplicity. Each of the phase boundary lines is determined by the level spectroscopy or the phenomenological renormalization analysis of numerical results of exact-diagonalization calculations. The resulting phase diagram on the Delta-D plane consists of four phases; the XY1 phase, the Haldane/ large-D phase, the intermediateD phase, and the Neel phase. The remarkable natures of the phase diagram are as follows: (1) there exists an intermediate-D phase which was predicted by Oshikawa in 1992; (2) the Haldane state and the large-D state belong to the same phase; (3) the shape of the phase diagram on the Delta-D plane is different from that considered so far. We note that this is the first report on the observation of the intermediate-D phase.

We investigate S = 1/2 quantum spin antiferromagnets on the triangular and Kagome lattices in a magnetic field, using the numerical exact diagonalization. We focus particularly on an anomalous magnetization behavior of each system at one-third the saturation magnetization. Critical exponent analyses suggest that it is a conventional magnetization plateau on the triangular lattice, while an unconventional phenomenon, called the magnetization ramp, occurs on the Kagome lattice.

We study ferrimagnetism in the ground state of the antiferromagnetic Heisenberg model on the spatially anisotropic kagome lattice, in which ferrimagnetism of the conventional Lieb-Mattis type appears in the region of weak frustration whereas the ground state is nonmagnetic in the isotropic case. Numerical diagonalizations of small finite-size clusters are carried out to examine the spontaneous magnetization. We find that the spontaneous magnetization changes continuously in the intermediate region between conventional ferrimagnetism and the nonmagnetic phase. Local magnetization of the intermediate state shows strong dependence on the site position, which suggests non-Lieb-Mattis ferrimagnetism.

The spin ladder systems have attracted a lot of interest in the field of low-dimensional physics. It is well known that the S = 1/2 two-leg spin ladder has a spin gap, while the three-leg one has a gapless spin liquid ground state. Some spin liquid behaviors were observed in the recent experiments of some frustrated systems; the distorted triangular lattice and kagome lattice antiferromagnets etc.. Thus we consider the S = 1/2 three-leg spin ladder system with the next-nearest-neighbor interaction to investigate the effect of frustration on the spin liquids. Using the exact numerical diagonalization of finite-cluster systems, we study the ground state of this system. The phase diagram with respect to some exchange interaction constants is presented. It is revealed that sufficiently large next-nearest-neighbor coupling leads to a ferrimagnetic phase, which has a frustration-induced spontaneous magnetization. In addition we find two spin liquid phases, one of which corresponds to a Neel-like spin configuration and the other a collinear spin configuration. As a result of the numerical study, we find a new phase which is different from three phases.

We numerically investigate the ground-state phase diagram of an S = 2 quantum spin chain with the XXZ and on-site anisotropies described by H = Sigma(j) ((SjSj+1x)-S-x vertical bar (SjSj+1y)-S-y vertical bar Delta S-j(z) + S-j+1(z)) + D Sigma(j)(S-j(z)) (2), where Delta denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and D the on-site anisotropy parameter. We restrict ourselves to the Delta > 0 and D > 0 case for simplicity. Our main purpose is to obtain the definite conclusion whether there exists or not the intermediate-D (ID) phase, which was proposed by Oshikawa in 1992 and has been believed to be absent since the DMRG studies in the latter half of 1990's. In the phase diagram with Delta > 0 and D > 0 there appear the XY state, the Haldane state, the ID state, the large-D (LD) state and the Neel state. In the analysis of the numerical data it is important to distinguish three gapped states; the Haldane state, the ID state and the LD state. We give a physical and intuitive explanation for our level spectroscopy method how to distinguish these three phases.

The thermodynamic properties and the magnetization under magnetic field at zero temperature of the spin-1/2 Heisenberg model on triangulated kagome lattice, which composed of two sublattices, are investigated by numerical exact diagonalization method for 18 and up to 27 spin clusters, respectively. The temperature dependence of magnetic susceptibility may be reproduced qualitatively with the weak ferromagnetic intersublattice nearest neighbor exchange coupling constant JAB as proposed by previous studies, although it is quantitatively insufficient in comparison with the experimental result. The magnetization under magnetic field shows the 5/9 plateau for every examined values of JAB, but 1/3 plateau, visible in the experiment, may be reproduced only for not so weak antiferromagnetic case of JAB. This discrepancy for JAB in those two qualities has also been recognized in previous studies on classical spin models and is not still resolved even for the present quantum spin system.

The magnetization process of the Heisenberg antiferromagnet on the kagome lattice is studied by numerical-diagonalization method. Though the magnetization plateau was considered to appear at the one-third of the magnetization saturation, recent reexamination of the magnetization process of the same model from another viewpoint of the field-derivative of the magnetization in finite-size data from the numerical-diagonalization calculation up to 36 sites suggests that the behavior at around one-third height of the saturation is clearly different from typical magnetization plateaux, which we should call the magnetiztaion ramp. The present study reports our new numerical-diagonalization result up to 39 sites, which reveals well the characteristics of the magnetization ramp. The behavior of the kagome lattice antiferromagnet is compared with the typical magnetization plateux of the Heisenberg antiferromagnet on the triangular lattice.

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.

Using the numerical exact diagonalization of finite-size clusters up to 39 spins, we investigate the magnetization process of the Kagome lattice antiferromagnet, as well as the triangular lattice antiferromagnet. A finite-size scaling analysis at 1/3 of the saturation magnetization indicates that an unconventional quantum phase transition, so called a magnetization ramp, occurs for the Kagome lattice antiferromagnet. In contrast, the triangular lattice antiferromagnet is revealed to exhibit a conventional 1/3 magnetization plateau. These conclusions are based on the estimated critical exponet delta defined as |m-m(c)| similar to |H-H-c|(1/delta). The exponents at the lower and higher field sides of m = 1/3 delta(-) and delta(+) are estimated as delta(-) = 1.9 +/- 1.0 and delta(+) = 0.5 +/- 0.2 for the Kagome kattice, while delta(-) = 1.0 +/- 0.2 and delta(+) = 0.8 +/- 0.2 for the triangular lattice.

By use of mainly numerical methods, we investigate the ground-state phase diagram of an S = 2 quantum spin chain with the XXZ and on-site anisotropies described by H = Sigma(j)(S-j(x) S-j+1(x) + S-j(y) S-j+1(y) + Delta S-j(z) S-j+1(z)) + D Sigma(j)(S-j(z))(2), where Delta denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and D the on-site anisotropy parameter. In the phase diagram with Delta > 0 and D > 0 there appear the XY phase, the Haldane/large-D (LD) phase, the intermediate-D (ID) phase, and the Neel phase. Among them the Ill phase was proposed by Oshikawa in 1992 and has been considered to be absent since the DMRG studies in the latter half of 1990's. And also, the Haldane state and the LD state belong to the same phase, which should be named Haldane/LD phase.

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.

The spin gap issue of the kagome lattice antiferromagnet is invesitigated by the finite size scaling analysis applied for the energy spectrum of the rhombic clusters calculated by the numerical exact diagonalization. The conclusion is that the kagome lattice antiferromagnet is gapless, as well as the triangular lattice one.

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.

The numerical diagonalization study on an extended t - J Holstein model, including the renormalization of the hole hopping t due to the phonon effect indicates that the breathing vibration of the in-plane oxygen can enhance the hole pairing for some parameters. (C) 2009 Published by Elsevier B.V.

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.

The magnetization process of the isotropic Heisenberg antiferromagnet on the kagome lattice is studied. Data obtained from the numerical-diagonalization method are reexamined from the viewpoint of the derivative of the magnetization with respect to the magnetic field. We find that the behavior of the derivative at approximately one-third of the height of the magnetization saturation is markedly different from that for the cases of typical magnetization plateaux. The magnetization process of the kagome-lattice antiferromagnet reveals a new phenomenon, which we call the "magnetization ramp''.

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.