链接杂质对一维量子Ising模型动力学性质的调控  

Effects of link-impurity on spin dynamics of one-dimensional quantum Ising model

作　　者：袁晓娟 YUAN Xiaojuan(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》2025年第3期170-181,共12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(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：自旋系统的动力学性质是量子统计和凝聚态理论研究的热点.本文利用递推方法,通过计算自旋关联函数及谱密度,研究了链接杂质对一维量子Ising模型动力学性质的调控效应.研究表明,链接杂质的出现打破了主体格点自旋耦合J和外磁场B之间原有的竞争关系,系统的动力学最终取决于链接杂质和主体格点自旋耦合的平均效应J^(-)、链接杂质的不对称程度及外磁场B的强度等多因素之间的协同作用.对于对称型链接杂质(J_(j-1)=J_(j)),随着杂质耦合强度的增大,在B≥J的情况下,系统的动力学出现了由集体模行为到中心峰值行为的交跨;在B_(j-1)≠J_(j),其杂质位型较多,可以提供更多的调控自由度,尤其当其中某个杂质耦合强度如J_(j-1)(或J_(j))较小时,通过调节另一个杂质耦合强度J_(j)(或J_(j-1))可以得到多种动力学行为之间的交跨;在B>J情况下,非对称型链接杂质的调控机制更为复杂,出现了与以往研究经验不符的交跨顺序,且出现了双频谱这种新的动力学模式.一般来讲,当平均自旋耦合J^(-)较弱或非对称型链接杂质的不对称程度较低时,系统倾向于呈现集体模行为;当J^(-)较强时,系统倾向于呈现中心峰值行为;但当非对称型链接杂质的不对称程度较明显时,谱密度倾向于呈双峰、多峰或双频谱特征.研究表明,链接杂质的调控结果更加丰富,且具有独特的调控优势,因此利用链接杂质来调控量子自旋系统的动力学不失为一种新的尝试.It is of considerable theoretical significance to study the effects of impurity on spin dynamics of quantum spin systems.In this paper,the dynamical properties of the one-dimensional quantum Ising model with symmetric and asymmetric link-impurity are investigated by the recursion method,respectively.The autocorrelation function C(t)=———√<σ_(j)^(x)(t)σ_(j)^(x)(0) and the associated spectral densityΦ(ω)=∫_(−∞)^(+∞)dte^(iωt)C(t)are calculated.The Hamiltonian of the Ising model with link-impurity can be written as H=−1/2(J_(j−1)σ_(j−1)^(x)σ_(j)^(x)+J_(j)σ_(j)^(x)σ_(j+1)^(x))−1/2J∑_(i≠j,j−1)^(N)σ_(i)^(x)σ_(i+1)^(x)−1/2B∑_(i)^(N)σ_(i)^(z).where J is the nearest-neighbor exchange coupling of the main spin chain,B denotes the external transverse magnetic field,σαi(α=x,y,z)are Pauli matrices at site i.The constant 1/2 is introduced for the convenience of theoretical deduction,and N is the number of spins.The so-called link-impurity J_(j)(J_(j−1))is randomly introduced,which denotes the exchange coupling between the j th spin and the(j+1)th spin(the(j–1)th spin).The symmetric link-impurity and asymmetric link-impurity correspond to the case of J_(j−1)=J_(j) and J_(j−1)≠J_(j),respectively.The periodic boundary conditions are assumed in the theoretical calculation.After introducing the link-impurity,the original competition between B and J in the pure Ising model is broken.The dynamic behavior of the system depends on synergistic effect of multiple factors,such as the mean spin coupling J^(-) between J and the link-impurity,the asymmetry degree between J_(j−1) and J_(j),and the strength of the external magnetic field.In calculation,the exchange couplings of the main spin chain are set to J≡1 to fix the energy scale.We first consider the effects of symmetric link-impurity.The reference values can be set to J_(j−1)=J_(j)<J(e.g.0.4,0.6 or 0.8)or J_(j−1)=J_(j)>J(e.g.1.2,1.6,2.0),which are called weak or strong impurity coupling.When the magnetic field B≥J(e.g.,

关 键 词：ISING模型 链接杂质 关联函数 谱密度 

分 类 号：O413[理学—理论物理] O469[理学—物理]