低温下XXZ反铁磁自旋链的自旋波谱

摘要

利用不变本征算符法及Dyson-Maleev（D-M）变换、点阵傅立叶变换、统计平均线性化近似等理论,研究XXZ反铁磁自旋链的自旋波谱变化规律,并推导出有限温度下XXZ反铁磁自旋链的自旋波能谱.在低温（kBT/Jz〈0.46）下,随着温度的升高磁振子软化逐渐加强;但是约化温度在0.46〈kBT/Jz〈0.621 3区域,随着温度的升高磁振子软化逐渐减弱.当kBT/Jz〉0.621 3时,非简谐近似下的反铁磁自旋链的自旋波能量,在第一布里渊区不出现软化现象,只有硬化现象,并且磁振子硬化与约化交换积分η=J┷/Jz无关.这表明XXZ反铁磁自旋链的自旋波谱与温度密切相关,并有2个转变温度kBT/Jz=0.46和kBT/Jz=0.621 3.%Using Invariant eigen-operator method and Dyson-Maleev（D-M） transform、lattice Fourier transform、statistical averaging linearization approximation etc.in this paper,the changing law of the spin waves Spectrum of XXZ Anti-ferromagnetic Spin Chain has been studied.Spin waves energy spectrum of XXZ anti-ferromagnetic spin chain under finite temperature has been derived.Under the low temperature（kBT/Jz0.46）,the magnon′s softening is reinforced with temperature rise.But in this range（0.46kBT/Jz0.621 3）,the magnon′s softening becomes weakening with the temperature rise.When kBT/Jz0.621 3,spin waves energy of anti-ferromagnetic spin chain at non-harmonic approximation only has hardening phenomenon and the softening does not happen.And the spin waves Spectrum′s hardening is irrelevant to reduced exchange integral（η=J┷/Jz）.It shows that spin waves Spectrum of XXZ Anti-ferromagnetic spin chain is closely relate to the temperature and has two transition temperature kBT/Jz=0.46 and kBT/Jz=0.621 3.