摘要
本文数值研究了在一维非厄米的硬核玻色模型中由随机两体耗散诱导的非厄米多体局域化现象.随着无序强度的增强,系统的能谱统计分布从AI+对称类向二维泊松系综过渡,多体本征态的归一化参与率展示了从有限值到接近零的转变,半链纠缠熵服从体积律到面积律的转变,动力学半链纠缠熵表现为从线性增长到对数增长的转变.数值结果表明,在该模型中由随机两体耗散诱导的非厄米多体局域化现象的鲁棒性.该研究结果为非厄米系统中多体局域化的研究提供了新的视角.
Abstract
Recent researches on disorder-driven many-body localization(MBL)in non-Hermitian quantum systems have aroused great interest.In this work,we investigate the non-Hermitian MBL in a one-dimensional hard-core Bose model induced by random two-body dissipation,which is described by(H)=L-1Σj[-J((b)ƚj+(b)j+1+(b)ƚj+1(b)j)+1/2(U-iγj)(n)j(n)j+1], with the random two-body loss γj-∈[0,W].By the level statistics,the system undergoes a transition from the AIƚsymmetry class to a two-dimensional Poisson ensemble with the increase of disorder strength.This transition is accompanied by the changing of the average magnitude(argument)(<r>)((-<cos θ>))of the complex spacing ratio,shifting from approximately 0.722(0.193)to about 2/3(0).The normalized participation ratios of the majority of eigenstates exhibit finite values in the ergodic phase,gradually approaching zero in the non-Hermitian MBL phase,which quantifies the degree of localization for the eigenstates.For weak disorder,one can see that average half-chain entanglement entropy(<S>)follows a volume law in the ergodic phase.However,it decreases to a constant independent of L in the deep non-Hermitian MBL phase,adhering to an area law.These results indicate that the ergodic phase and non-Hermitian MBL phase can be distinguished by the half-chain entanglement entropy,even in non-Hermitian system,which is similar to the scenario in Hermitian system.Finally,for a short time,the dynamic evolution of the entanglement entropy exhibits linear growth with the weak disorder.In strong disorder case,the short-time evolution of(S(t))shows logarithmic growth.However,when t≥102,(S(t))can stabilize and tend to the steady-state half-chain entanglement entropy((S)0).The results of the dynamical evolution of(S(t))imply that one can detect the occurrence of the non-Hermitian MBL by the short-time evolution of(S(t)),and the long-time behavior of(S(t))signifies the steady-state information.
基金项目
国家自然科学基金(12375016)
山西省基础研究计划(20210302123442)
北京凝聚态物理国家研究中心开放课题()
山西"1331工程"重点学科建设计划()
维普
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