Hiroki Nakano

Abstract The magnetization process of the antiferromagnetic chain with coupling and single-ion anisotropies is investigated using numerical diagonalization of finite-size clusters and level spectroscopy analysis. Various magnetization plateaux are found at 1/5, 2/5, 3/5, and 4/5 of the saturation magnetization. plateaux without translational symmetry breaking are predicted to occur at 1/5 and 3/5 magnetization. A symmetry-protected topological plateau phase is found at 3/5 magnetization, but not at 1/5. In addition translational-symmetry-broken plateaux induced by large coupling anisotropy are found at 1/5, 2/5, 3/5, and 4/5 magnetization. Phase diagrams at 1/5, 2/5, 3/5, and 4/5 of the saturation magnetization are obtained. Magnetization curves for several representative anisotropies are also presented, together with the corresponding magnetic phase diagrams.

Abstract Recent advances in the orthogonal-dimer spin- Heisenberg antiferromagnet are reviewed. This model has been examined for more than 40 years since it was originally studied by Shastry and Sutherland. The discovery of SrCu (BO ) as a good candidate material for the system led to a considerable advancement in subsequent research. In the case when is larger than 1/2, however, the elucidation of the properties of the system was relatively delayed. In the ground state of general- systems, interesting quantum phase transitions occur not only for . In this article, the systematic behavior depending on which has been recently clarified by unbiased and numerical computational calculations is reviewed. The effects due to spin anisotropy as determined from experimental and theoretical results are also overviewed. We also mention recent developments for the system.

Abstract The spin- S Heisenberg antiferromagnet on the two-dimensional lattice is investigated for S = 1/2 and S = 1. We consider interaction at isolated dimers ( J _d ) and interaction bonds that form the bounce lattice ( J _b ). For J _d = J _b , the system is reduced to the maple-leaf-lattice antiferromagnet. We primarily conduct highly parallelized numerical diagonalization to examine the spin excitation gap above the ground state for various J _b / J _d cases. For S = 1/2, we report calculations for a 42-site cluster that has not been previously treated. The S = 1 case is examined for the first time for clusters up to 24 sites. Regardless of whether S = 1/2 or 1, we find that the system has a gapped nature for small J _d / J _b and becomes gapless at J _d / J _b ∼ 1.4. For S = 1, we also find that another gapped region appears between the gapless case at J _d / J _b ∼ 1.4 and the boundary of the exact-dimer phase.