Spin chains with bond alternation

Abstract

The anisotropic spin chains with bond alternation expressed by the Hamiltonian equation were investigated. The ground state phase diagram was obtained from the data of the numerical diagonalization of the Hamiltonian for S = 1 case using a level spectroscopy. The phase diagrams were found to be quite different from that obtained by Singh and Gelfand, for the reason that a tetracritical point between the XY, dimer, Haldane and Neel phases was not existed in the phase diagram. The plateau of the magnetization curve at M value of a half of the saturation magnetization was investigated and discussed in connection with the critical value. The Berezinskii-Kosterlitz-Thouless transition between the dimer and XY phase for S = 1/2 case was studied using the numerical diagonalization and the level spectroscopy. The dimer-XY boundary of this work has been well agreed with the previous work.

Hamilton方程式で表される結合交代を有する異方性スピン鎖を検討し、準位分光法を用いてS=1のときのハミルトニアンの数値対角化のデータから基底状態相図を得た。この相図には、XY、2量体、HaldaneおよびNeel相間の4臨界点が存在しないという理由で、SinghおよびGelfandにより作成された相図に比してかなり異なることが分かった。M値が飽和磁化の1/2のときの磁化曲線のプラトーを検討し、臨界値の関連で論じた。S=1/2のときの、2量体とXY相の間のBerezinskii-Kosterlitz-Thouless転移を数値対角化および準位分光を用いて研究した。2量体、XY境界は前に得られた結果と良く一致した。