三模型随机场对一维量子Ising模型动力学性质的调控  

Effects of trimodal random magnetic field on spin dynamics of quantum Ising chain

作　　者：袁晓娟 Yuan Xiao-Juan(College of Physics and Electronic Engineering,Qilu Normal University,Jinan 250200,China)

机构地区：[1]齐鲁师范学院物理与电子工程学院,济南250200

出　　处：《物理学报》2023年第8期303-312,共10页Acta Physica Sinica

基　　金：山东省自然科学基金(批准号:ZR2021MA073);山东省高等学校科技计划项目(批准号:J18KB104);齐鲁师范学院青年博士支持计划(批准号:QBJH19-0006)资助的课题.

摘　　要：量子自旋系统在外磁场下的动力学性质一直是凝聚态理论和统计物理研究的热点.本文利用递推关系方法,通过计算系统的自旋关联函数及其对应的谱密度,研究了三模型随机外场对一维量子Ising模型动力学性质的调控效应.在三模型随机横场下,利用r分支引入了非磁性杂质,研究表明:非磁性杂质使得系统的低频响应得到保持,中心峰值行为更加明显;非磁性杂质与横场之间的竞争能激发出新的频率响应,呈现多峰行为;但较多的非磁性杂质最终会限制系统对横场的响应.此外,研究还发现随机横场的三模分布参数满足qB_(q)=pB_(p)这一条件,是使中心峰值行为得到保持的有利条件.在三模型随机纵场下,r分支仅仅起到调节纵场强度的作用,且r分支所占比重的增大不利于低频响应,与三模型随机横场下r分支的调控作用是相反的.It is of fundamental importance to know the dynamics of quantum spin systems immersed in external magnetic fields.In this work,the dynamical properties of one-dimensional quantum Ising model with trimodal random transverse and longitudinal magnetic fields are investigated by the recursion method.The spin correlation function C(t)=σ_(j)^(x)(t)σ_(j)^(x)(0)^(-)and the corresponding spectral densityΦ(ω)=∫_(−∞)^(+∞)dte^(iωt)C(t)are calculated.The model Hamiltonian can be written asH=−12J∑_(i)^(N)σ_(i)^(x)σ_(i)^(x)+1−12∑_(i)^(N)B_(iz)σ_(i)^(z)−12∑_(i)^(N)B_(ix)σ_(i)^(x),whereσαi(α=x,y,z)are Pauli matrices at site i,Jis the nearest-neighbor exchange coupling.B_(iz) and B_(ix) denote the transverse and longitudinal magnetic field,respectively.They satisfy the following trimodal distribution,ρ(B_(iz))=pδ(B_(iz)−B_(p))+qδ(B_(iz)−B_(q))+rδ(B_(iz)),ρ(B_(ix))=pδ(B_(ix)−B_(p))+qδ(B_(ix)−B_(q))+rδ(B_(ix)).The value intervals of the coefficients p,q and r are all[0,1],and the coefficients satisfy the constraint condition p+q+r=1.For the case of trimodal random B_(iz)(consider B_(ix)≡0 for simplicity),the exchange couplings are assumed to be J≡1 to fix the energy scale,and the reference values are set as follows:B_(p)=0.5<J and B_(q)=1.5>J.The coefficient r can be considered as the proportion of non-magnetic impurities.When r=0,the trimodal distribution reduces into the bimodal distribution.The dynamics of the system exhibits a crossover from the central-peak behavior to the collective-mode behavior as q increases,which is consistent with the value reported previously.As r increases,the crossover between different dynamical behaviors changes obviously(e.g.the crossover from central-peak to double-peak when r=0.2),and the presence of non-magnetic impurities favors low-frequency response.Owing to the competition between the non-magnetic impurities and transverse magnetic field,the system tends to exhibit multi-peak behavior in most cases,e.g.r=0.4,0.6 or 0.8.However,the multi-peak

关 键 词：ISING模型 三模分布 自旋关联函数 谱密度 

分 类 号：O469[理学—凝聚态物理]