中野 博生

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.

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.

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 the ground-state properties of the S = 1/2 antiferromagnetic Heisenberg model on the Union Jack strip lattice by using the exact-diagonalization and density matrix renormalization group methods. We confirm a region of a magnetization state intermediate between the N,el-like spin liquid state and the conventional ferrimagnetic state of a Lieb-Mattis type. In the intermediate state, we find that the spontaneous magnetization changes gradually with respect to the strength of the inner interaction. In addition, the local magnetization clearly shows an incommensurate modulation with long-distance periodicity in the intermediate magnetization state. These characteristic behaviors lead to the conclusion that the intermediate magnetization state is a non-Lieb-Mattis ferrimagnetic one. We also discuss the relationship between the ground-state properties of the S = 1/2 antiferromagnetic Heisenberg model on the original Union Jack lattice and those on our strip lattice.

We have succeeded in synthesizing organic biradical crystals of m-Ph-V 2 [= 1,3-bis-(1,5-diphenylverdazyl-3- yl)benzene]. The intra and intermolecular interactions, which are deduced from the molecular packing in the crystal, are considered to form an alternating double chain. We evaluated the intramolecular ferromagnetic (FM) interaction from an analysis of the magnetic susceptibility of isolated m-Ph-V2 molecules. We analyzed the magnetic susceptibility and magnetization curves of the crystals by the quantum Monte Carlo method and successfully explained these properties using an S = 1=2 FM alternating double chain model, which consists of antiferromagnetically coupled FM alternating chains. In addition, the magnetic susceptibility and specific heat showed anomalous behavior at TN = 1.9 K, which indicates the magnetic phase transition to an antiferromagnetically ordered state. © 2013 The Physical Society of Japan.

We have succeeded in synthesizing single crystals of a new organic radical 3-Cl-4-F-V [3-(3-chloro-4-fluorophenyl)-1,5-diphenylverdazyl]. Through the ab initio molecular orbital calculation and the analysis of the magnetic properties, this compound was confirmed to be the first experimental realization of an S=1/2 spin-ladder system with ferromagnetic leg interactions. The field-temperature phase diagram indicated that the ground state is situated very close to the quantum critical point. Furthermore, we found an unexpected field-induced successive phase transition, which possibly originates from the interplay of low dimensionality and frustration. © 2013 American Physical Society.

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.

We successfully synthesized verdazyl biradical crystals of p-BIP-V 2 [4,4′-bis(1,5-diphenylverdazyl-3-yl)biphenyl]. Two types of intermolecular interactions are deduced from the spin-density distribution and molecular packing in the crystal, and these interactions are considered to result in the formation of a honeycomb lattice. The ab initio molecular orbital calculation also indicated such an exchange network of intermolecular interactions. The intramolecular interaction acts as a diagonal bridge across the honeycomb lattice to form a square lattice. We evaluated the intramolecular antiferromagnetic (AF) interaction J1 to be about 8.8 K from an analysis of the magnetic susceptibility of isolated p-BIP-V 2 molecules in terms of an isolated S = 1/2 AF dimer. We analyzed the magnetic susceptibility of the crystals using the quantum Monte Carlo method. Consequently, two types of intermolecular AF interactions, J2 and J3, were found to be almost comparable and about 4.5 times larger than the intramolecular interaction J1. Thus, we confirmed that p-BIP-V2 has a slightly distorted S=1/2 honeycomb-like lattice. © 2013 American Physical Society.

We study the magnetization curve of the Heisenberg model on the quasi-one-dimensional Kagome-strip lattice that shares the same lattice structure in the inner part with the two-dimensional Kagome lattice. Our numerical calculations based on the density matrix renormalization group method reveal that the system shows several magnetization plateaus between zero magnetization and the saturated one; we find the presence of the magnetic plateaus with the n/7 height of the saturation for n=1,2,3,4,5 and 6 in the S=1/2 case, whereas we detect only the magnetic plateaus of n=1,3,5 and 6 in the S=1 case. In the cases of n=2,4 and 6 for the S=1/2 system, the Oshikawa-Yamanaka-Affleck condition suggests the occurrence of the translational symmetry breaking (TSB). We numerically confirm this non-trivial TSB in our results of local magnetizations. We have also found that the macroscopic jump appears near the saturation field irrespective of the spin amplitude as well as the two-dimensional Kagome model. © 2012 Springer Science+Business Media, LLC.

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.

We successfully synthesized verdazyl biradical crystals of p-BIP-V-2 [4,4'-bis(1,5-diphenylverdazyl-3-yl) biphenyl]. Two types of intermolecular interactions are deduced from the spin-density distribution and molecular packing in the crystal, and these interactions are considered to result in the formation of a honeycomb lattice. The ab initio molecular orbital calculation also indicated such an exchange network of intermolecular interactions. The intramolecular interaction acts as a diagonal bridge across the honeycomb lattice to form a square lattice. We evaluated the intramolecular antiferromagnetic (AF) interaction J(1) to be about 8.8 K from an analysis of the magnetic susceptibility of isolated p-BIP-V-2 molecules in terms of an isolated S = 1/2 AF dimer. We analyzed the magnetic susceptibility of the crystals using the quantum Monte Carlo method. Consequently, two types of intermolecular AF interactions, J(2) and J(3), were found to be almost comparable and about 4.5 times larger than the intramolecular interaction J(1). Thus, we confirmed that p-BIP-V-2 has a slightly distorted S = 1/2 honeycomb-like lattice. DOI: 10.1103/PhysRevB.87.125120

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/J1~0.1. © 2013 WILEY-VCH Verlag GmbH &amp Co. KGaA, Weinheim.

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.

We study the ground-state properties of the S = 1/2 Heisenberg models on the quasi-one-dimensional kagome strip lattices by the exact diagonalization and density matrix renormalization group methods. The models with two different strip widths share the same lattice structure in their inner part with the spatially anisotropic two-dimensional kagome lattice. When there is no magnetic frustration, the well-known Lieb-Mattis ferrimagnetic state is realized in both models. When the strength of magnetic frustration is increased, on the other hand, the Lieb-Mattis-type ferrimagnetism is collapsed. We find that there exists a non-Lieb-Mattis ferrimagnetic state between the Lieb-Mattis ferrimagnetic state and the nonmagnetic ground state. The local magnetization clearly shows an incommensurate modulation with long-distance periodicity in the non-Lieb-Mattis ferrimagnetic state. The intermediate non-Lieb-Mattis ferrimagnetic state occurs irrespective of strip width, which suggests that the intermediate phase of the two-dimensional kagome lattice is also the non-Lieb-Mattis-type ferrimagnetism.

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 Cu9X2(cpa)(6)center dot nH(2)O (X = F, Cl, Br; cpa = the anion of 2-carboxypentonic acid) is given by the Heisenberg model with the antiferromagnetic next-nearest-neighbor 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.

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.

We investigate the excitation energies of hyperbolically deformed S = 1 spin chains, which are specified by the local energy scale f(j) = cosh j lambda, where j is the lattice index and lambda is the deformation parameter. The elementary excitation is well described by a quasi-particle hopping model, which is also expressed in the form of hyperbolic deformation. It is possible to estimate the excitation gap Delta in the uniform limit lambda -> 0 by finite size scaling with respect to the system size L and the deformation parameter lambda.

We report the results of magnetization and specific heat measurements on Ba3NiSb2O9, which is a quasi-two-dimensional spin-1 triangular-lattice antiferromagnet. We observed a nonclassical magnetization plateau at one-third of the saturation magnetization that is driven by spin frustration and quantum fluctuation. Exact diagonalization for a 21-site rhombic cluster was performed to analyze the magnetization process. Experimental and calculated results agree well.

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.

The ground-state properties of the S = 1/2 frustrated Heisenberg spin chain with interactions up to fourth nearest neighbors are investigated by the exact-diagonalization method and density matrix renormalization group method. Our numerical calculations clarify that the ferrimagnetic state is realized in the ground state in spite of the fact that a multi-sublattice structure in the shape of the system is absent. We find that there are two types of ferrimagnetic phases: one is the well-known ferrimagnetic phase of the Lieb-Mattis type and the other is the nontrivial ferrimagnetic phase that is different from that of the Lieb-Mattis type. Our results suggest that a multi-sublattice structure of the shape is not necessarily required for the occurrence of ferrimagnetism.

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 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.

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.

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.

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.

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 study ground-state properties of the S = 1/2 Heisenberg model on the Kagome strip lattice by using exact-diagonalization and density matrix renormalization group methods. When the strength of magnetic frustration is tuned, we find from our numerical calculations that there exists an intermediate phase between the non-magnetic phase and the ferrimagnetic phase of the well-known Lieb-Mattis type and that the local magnetization shows an inocommensurate modulation with long-distance periodicity in the intermediate phase. Since the present model shares the same lattice structure in its inner part with the spatially anisotropic two-dimensional Kagome lattice in which an intermediate phase with a similar behavior is certainly observed, the intermediate phases of these models are the ferrimagnetic one of the unconventional non-Lieb-Mattis type.

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.

We introduce a one-parameter deformation for one-dimensional quantum lattice models, the hyperbolic deformation, where the scale of the local energy is proportional to cosh lambda j at the jth site. From the quantum-classical correspondence with a two-dimensional classical system, it is expected that the deformation does not modify the ground state conspicuously, if there is a finite excitation gap. Under this situation, the excited quasi particle is weakly confined around the center of the system. We derive scaling relations among the mean-square width < w(2)> of confinement, energy correction to the excitation gap Delta, and deformation parameter lambda. This scaling is useful for the extraction of the bulk excitation gap in the limit lambda = 0.

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''.

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.

We carry out finite-size extrapolations of numerical-diagonalization data of the S=1 Heisenberg chain having a nonzero energy gap between the unique singlet ground state and the first excited state, namely the Haldane gap. Very precise estimates of the ground-state energy per site E-g/N = -1.4014840447(39) and the staggered component of the magnetic structure factor S-pi = 3.864356(31) at T=0 are successfully obtained from the finite-size data of system sizes up to N = 24 under the twisted boundary condition by the sequence interval squeeze method, which was applied to a precise estimation of the Haldane gap by Nakano and Terai [J. Phys. Soc. Jpn. 78 (2009) 014003]. The present estimates are compared with other estimates in previous studies from various methods including the quantum Monte Carlo simulation and the density matrix renormalization group calculation.

Thermal expansion of two-dimensional itinerant nearly ferromagnetic metal is investigated according to the recent theoretical development of magneto-volume effect for the three-dimensional weak ferromagnets. We particularly focus on the T-2-linear thermal expansion of magnetic origin at low temperatures, so far disregarded by conventional theories. As the effect of thermal spin fluctuations we have found that the T-linear thermal expansion coefficient shows strong enhancement by assuming the double Lorentzian form of the non-interacting dynamical susceptibility justified in the small wave-number and low frequency region. It grows faster in proportional to y(-1/2) as we approach the magnetic instability point than two-dimensional nearly antiferromagnetic metals with ln(1/y(s)) dependence, where y and y(s) are the inverses of the reduced uniform and staggered magnetic susceptibilities, respectively. Our result is consistent with the Gruneisen's relation between the thermal expansion coefficient and the specific heat at low temperatures. In 2-dimensional electron gas we find that the thermal expansion coefficient is divergent with a finite y when the higher order term of non-interacting dynamical susceptibility is taken into account.

We propose two methods of estimating a systematic error in extrapolation to the infinite-size limit in the study of measuring the Haldane gaps of the one-dimensional Heisenberg antiferromagnet with the integer spin up to S = 5. The finite-size gaps obtained by numerical diagonalizations based on Lanczos algorithm are presented for sizes that have not previously been reported. The changes of boundary conditions are also examined. We successfully demonstrate that our methods of extrapolation work well. The Haldane gap for S = 1 is estimated to be 0.4104789 +/- 0.0000013. We successfully obtain the caps up to S = 5, which make us confirm the;asymptotic formula of the Haldane gap in S -> infinity.

We have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multipoint correlation function characterizing the ground state. This work presents a successful application of this procedure to the string order parameter of the S=1 XXZ chain with uniaxial single-ion anisotropy. The finite-size string correlation function is estimated by the density-matrix renormalization-group method. We focus on the gradient of the inverse-system-size dependence of the correlation function on a logarithmic plot. This quantity shows that the finite-size scaling sensitively changes at the critical point. The behavior of the gradient with increasing system size is divergent, is stable at a finite value, or rapidly decreases to zero when the system is in the disordered phase, at the critical point, or in the ordered phase, respectively. The analysis of the finite-size string correlation functions allows precise determination of the boundary of the Haldane phase and estimation of the critical exponent of the correlation length. Our estimates of the transition point and the critical exponents, which are determined only by the ground-state quantities, are consistent with results obtained from the analysis of the energy-level structure. Our analysis requires only the correlation functions of several finite sizes under the same condition as a candidate for the long-range order. The quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned. This work will assist in the development of a method for directly observing quantum phase transitions.

We have found a set of order parameters that characterize the plateau state of the (S = 1, 1/2) spin chain system. The order parameters are regarded as extensions of the string order parameter of the S = I antiferromagnetic Heisenberg spin chain. The extension is made by mapping the S, = 1/2 (S-z = -1/2) state of an S = 1 /2 spin onto the S, = 0 (S-z = - 1) state of an S = I spin. Numerical data indicate that, when single-ion anisotropy D is introduced, all the order parameters decrease continuously and vanish in the large-D region. Our estimate of the critical value D, for the phase transition agrees well with the phase boundary determined by a previous level spectroscopy analysis. We present estimates of three critical exponents that are associated with the order parameters. A scaling relation between the exponents holds well in the present system.

To determine the effective spin model of the nano scale ferrimagnetic ring [Mn(hfac)(2)NITPh](6) abbreviated as Mn6R6, we propose a new criterion that the model should reproduce spatial configuration of the local spin densities of the reference system calculated by the hybrid density functional theory. The new prescription to Mn6R6 is successfully applied to clarify that the effective spin model consists of not only the nearest neighbor antiferromagnetic interaction but also the next nearest neighbor antiferromagnetic interaction which causes frustration in the spin system. The present result suggests that the spatial configuration of the spin densities gives an essential information for the determination of the effective spin model. (c) 2006 Elsevier Ltd. All rights reserved.