Effects of a transverse field and non-linear excitations in a one-dimensional quantum spin chain

Abstract

To reveal the general properties of the domain-wall excitation, the S = 1/2 antiferromagnetic XXZ chain was studied under a symmetry-breaking field. The low-lying spectrum of the finite-spin systems was calculated using the exact diagonalization method and the characteristic behavior of the field dependence of the energy gap caused by the domain-wall excitations was found. Furthermore, the field dependence of the energy gap in the vicinity of the disorder field was studied in detail. The shift of wavevector was observed in the anisotropic XY model in the transverse field. The excitation spectrum of this system is same as the free fermion excitation spectrum, which corresponds to the domain-wall along the capital Z-direction and has a finite gap. From the analogy of the XY model, it was concluded that the low energy property of this system can be described in terms of the domain-wall excitation.

分域壁励起の一般的性質を明らかにするために対称性破れの磁場下でのS=1/2反強磁性XXZ鎖を研究した。この研究のために、厳密対角化法を用いて有限スピン系の低励起スペクトルを計算し、分域壁励起によって生じたエネルギーギャップの磁場依存性の特徴的挙動を見いだした。更に転移磁場付近におけるエネルギーギャップの磁場依存性を詳細に研究した。波数ベクトルの移動は横磁場内の異方性をXY模型で認めた。この系の励起スペクトルはZ方向に沿った分域壁に相当し、有限ギャップをもつ自由フェルミオン励起スペクトルと同じである。XY模型の類推から、この系の低エネルギー特性は分域壁励起によって記述可能であると結論した。