One dimensional S = 1 XXZ chains with uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. The numerical data are analyzed using conformal field theory, the level spectroscopy, phenomenological renormalization group and finite size scaling method. We thus present the first quantitatively reliable ground state phase diagram of this model. The ground states of this model contain the Haldane phase, large-D phase, Néel phase, two XY phases and the ferromagnetic phase. There are four different types of transitions between these phases: the Brezinskii-Kosterlitz-Thouless type transitions, the Gaussian type transitions, the Ising type transitions and the first order transitions. The location of these critical lines are accurately determined.

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The magnetization process of the S = 1 and 1/2 kagomé Heisenberg antiferromagnet is studied by means of the numerical exact diagonalization method. It is found that the magnetization curve at zero temperature has a plateau at 1/3 of the full magnetization. In the presence of √ 3 × √ 3 lattice distortion, this plateau is enhanced and eventually the ferrimagnetic state is realized. There also appear the minor plateaux above the main plateau. The physical origin of these phenomena is discussed.KEYWORDS: kagomé Heisenberg antiferromagnet, numerical diagonalization, magnetization plateau §1. IntroductionThe kagomé Heisenberg antiferromagnet (KHAF) has been extensively studied theoretically and experimentally because of the interest in the interplay of the strong quantum fluctuation and the highly frustrated nature of the lattice structure. So far, most of the attempts have been focused on the ground state and low lying excitations of the uniform KHAF. In both S = 1/2 1, 2, 3, 4) and S = 1 5) cases, it is known that the ground state is a spin singlet state and the magnetic excitation has a finite energy gap. In the S = 1/2 case, there are a number of singlet excitations below the first triplet excitation possiblly down to zero energy in the thermodynamic limit. 4)On the other hand, the singlet excitations also have finite energy gaps in the S = 1 case. The present author proposed the hexagonal singlet solid (HSS) picture for the ground state of S = 1 KHAF. 5)In the present work, we first investigate the magnetization process of this model. As examples of the frustrated quantum magnets, the magnetization process of the triangular Heisenberg magnet is widely studied. 6, 8, 7)The magnetization plateau at one-third of the full magnetization is well estabilshed in the Ising-like classical Heisenberg model as a typical example of the 'classical' magnetization plateau. 7) Although this plateau can be well understood in terms of the classical spin configuration, it has been observed even in the isotropic Heisenberg model with S = 1/2 which has strong quantum fluctuation.8) On the other hand, the honeycomb lattice S = 1/2 Heisenberg antiferromagnet has no plateau. 8)In this context, it is interesting to investigate the case of kagomé lattice which has the triangles and hexagons at the same time.As a real material, Wada and coworkers 11,12,13) have investigated the magnetic behavior of m-MPYNN·BF 4 which can be regarded as the S = 1 kagomé antiferromagnet. * e-mail: hida@phy.saitama-u.ac.jp This material, however, undergoes a structual transformation at 128.7K to the distorted phase with √ 3 × √ 3 structure.14) Motivated by this observation, we further investigate the effect of such lattice distortion to the ground state and magnetization process in both S = 1/2 and S = 1 cases. We find that the plateau is enhanced by the lattice distortion and eventually the ferrimagnetic ground state is realized. This paper is organized as follows: In §2, the model Hamiltonian is presented. The numerical results for the magnetization curves a...

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Low energy spectrum of the S = 1 kagomé Heisenberg antiferromagnet (KHAF) is studied by means of exact diagonalization and the cluster expansion. The magnitude of the energy gap of the magnetic excitation is consistent with the recent experimental observation for m-MPYNN·BF4. In contrast to the S = 1/2 KHAF, the non-magnetic excitations have finite energy gap comparable to the magnetic excitation. As a physical picture of the ground state, the hexagon singlet solid state is proposed and verified by variational analysis.

The competition between quantum and classical magnetization plateaus of S = 1/2 frustrated Heisenberg chains with modified exchange couplings is investigated. The conventional S = 1/2 frustrated Heisenberg chain is known to exhibit a 3-fold degenerate ↑↓↑ -type classical plateau at 1/3 of the saturation magnetization accompanied by the spontaneous Z3 translational symmetry breakdown. The stability of this plateau phase against period 3 exchange modulation which favors the •-• ↑-type quantum plateau state (•-• = singlet dimer) is studied by bosonization, renormalization group and numerical diagonalization methods. The ground state phase diagram and the spin configuration in each phase are numerically determined. The translationally invariant Valence Bond Solid-type model with 4-spin and third neighbor interactions, which has the exact •-• ↑-type quantum plateau state, is also presented. The phase transition to the classical ↑↓↑ -type ground state is also observed by varying the strength of 4-spin and third neighbor interactions. The relation between these two types of models with quantum plateau states is discussed.

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