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The magnetization process of the S = 1 and S = 2 spin alternating ferrimagnetic chain with the single-ion anisotropies is investigated by the numerical exact diagonalization and the density matrix renormalization group method. It is found that the mechanism of the 2/3 magnetization plateau formation due to quantum effects depends on the anisotropy constants. The obtained phase diagram of the 2/3 plateau is revealed to include three different phases.

By use of mainly the exact diagonalization and the level spectroscopy method, we investigate the ground-state phase diagrams of the $S=1/2$ distorted diamond type quantum spin chain with the monomer-monomer interactions and/or ferromagnetic interactions for the zero magnetic field case, as well as the $M=M_{\rm s}/3$ case and the $M=(2/3)M_{\rm s}$ case, where $M$ is the total magnetization and $M_{\rm s}$ is the saturation magnetization. The magnetization plateau at $M=M_{\rm s}/3$ vanishes in the region where the ferromagnetic interaction is rather strong. The monomer-monomer interaction remarkably stabilizes the magnetization plateau at $M=(2/3)M_{\rm s}$.

Employing mainly numerical methods, we explore the ground-state phase diagram of an anisotropic S = 1/2 ladder, in which leg interactions are uniform and isotropic, while rung interactions are alternating and have a common Ising-t.ype anisotropy. We determine the phase diagram in the case where Jleg = 0.2 (antiferromagnetic), Jrung = —1.0 (ferromagnetic) and |J'rung| ≤ 1.0, the first one being the magnitude of the leg interaction and the second and third ones those of the rung interactions, which are alternating. It is emphasized that the system has a frustration when J'rung is positive. We find that., in the frustrated region, the Haldane state appears as the ground state even when the Ising character of rung interactions is strong. This appearance of the Haldane phase is contrary to the ordinary situation, and it is called the inversion phenomenon concerning the interaction anisotropy. We also find that an incommensurate state becomes the ground state in a portion of the Haldane phase region.

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 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.

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 = Σj(SjxSj+1x + SyjSyj+1 + ΔSzjSzj+1 + D Σj(Szj)2, where Δ denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and D the on-site anisotropy parameter. In the phase diagram with Δ > 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 ID 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.

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.

The distorted diamond chain has attracted a lot of interest, since the compound Cu3(CO3)2(OH)2, so-called azurite, was revealed to be a good candidate for this system. Although several theoretical studies were performed, the strong anisotropy observed in the magnetization measurement of azurite has not been explained very well. To solve the mechanism of this anisotropy, we introduce the Dzyaloshinsky-Moriya (DM) interaction suitable for the crystal symmetry of azurite. The numerical diagonalization study on this realistic model indicates that the anisotropy in the experimental magnetization curve would be reproduced with sufficiently large DM interaction. We also propose a mechanism of the field-induced incommensurate order, which was observed above the 1/3 magnetization plateau by the NMR measurement.

The magnetization process of the S = 1/2 spin ladder system with ferromagnetic rung exchange interaction is investigated by the numerical exact diagonalization of finite-size clusters. It is found that in the presence of an easy-axis anisotropy the system exhibits a two-step field induced phase transition corresponding to the spin flop. Due to large quantum fluctuation, each step is a second-order transition and the second step occurs between two different Tomonaga-Luttinger liquid phases. Some phase diagrams are also presented.

Employing various numerical methods, we determine the ground-state phase diagram of an (S, S') = (1, 2) spin-alternating chain with antiferromagnetic nearest-neighboring exchange interactions and uniaxial single-ion anisotropies. The resulting phase diagram consists of eight kinds of phases including two phases which accompany the spontaneous breaking of the translational symmetry and a ferrimagnetic phase in which the ground-state magnetization varies continuously with the uniaxial single-ion anisotropy constants for the S=1 and S =2 spins. The appearance of these three phases is attributed to the competition between the uniaxial single-ion anisotropies of both spins.