Sakai Toru

Abstract The spin-S Heisenberg antiferromagnet on the orthogonal-dimer lattice is studied. In most of the investigations of the antiferromagnet on this lattice beginning with the study by Shastry and Sutherland, the case has intensively been treated. In the present study, the cases of S = 1 and 3/2 are particularly treated by the numerical-diagonalization method based on the Lanczos algorithm applied to finite-size clusters. We successfully capture the edge of the exact-dimer phase and that of the Néel-ordered phase. A significant finding is the existence of an intermediate phase between both the edges irrespective of spin-S.

The magnetization processes of the S = 3/2 and S = 2 antiferromagnetic chains with the biquadratic interaction are investigated using the numerical diagonalization of the finite-size cluster. It is found that the system does not exhibit the spin nematic phase, which was predicted to occur for the S = 1 antiferromagnetic chain. Instead, the present analysis reveals that the quantum spin triatic and quatic liquid phases appear below the saturation magnetization for sufficiently large negative biquadratic interaction, for S = 3/2 and S = 2 chains, respectively. In addition it is also found that the magnetization jump up to the saturation magnetization appears for the small negative biquadratic interaction. The phase diagrams with respect to the negative biquadratic interaction and the magnetization are presented for the S = 3/2 and S = 2 antiferromagnetic chains.