非厄米耦合链中的局域化转变  

Localization transition in non-Hermitian coupled chain

作　　者：古燕 陆展鹏 Gu Yan;Lu Zhan-Peng(Shanxi Vocational University of Engineering Science and Technology,Jinzhong 030619,China;State Key Laboratory of Quantum Optics and Quantum Optics Devices,Institute of Theoretical Physics,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西工程科技职业大学,晋中030619 [2]山西大学理论物理研究所,量子光学与光量子器件国家重点实验室,太原030006

出　　处：《物理学报》2024年第19期260-267,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12205176);高层次人才科研启动项目(批准号:RCK202231)资助的课题。

摘　　要：本文研究了受复数准周期势调制的一维耦合链中系统的局域化特性.通过研究发现随着无序强度增大的过程中,系统会经历一个从完全扩展相到中间相,再转变成完全局域相的局域转变.通过数值求解不同的序参量证明了转变过程中完全扩展相,具有迁移率边的中间相和完全局域相的存在.并且通过解析推导,可以精确求解出扩展相到中间相和中间相到局域相的局域化转变点.此外,还研究了系统能谱实-复转变与局域化转变之间的关系,发现系统能谱可以经历两次实复转变.即从完全扩展相到中间相的转变中,会发生第一次实复转变,部分能谱从实数谱转变为复数谱,但是部分能谱依然保持为实数谱.当系统从中间相转变为完全局域相时,系统能谱会完全转变为复数谱.该研究结果为一维耦合链系统中局域化转变和实复转变的研究提供了一些新的理解和参考.In this paper,we study the properties of a coupled chain modulated by the quasiperiodic complex potential.It is found that as the disorder strength increases,the system undergoes a localization transition from a fully extended phase to an intermediate phase,and then to a fully localized phase.The numerical solving of order parameters such as the average inverse participation ratio and the average normalized participation ratio,demonstrate that the fully extended phase,the intermediate phase with mobility edges,and the fully localized phase are all existent during the transition.The scalar analysis of the normalized participation ratio,confirms the stable existence of three different localization phases in the system.Moreover,the analytical derivation,shows that the localization transition from the extended phase to the intermediate phase and from the intermediate phase to the localized phase can be precisely determined.In addition,the local phase diagram of the system is also obtained by numerical calculation,as shown in Fig.(a).The regions for the extended,intermediate and localized phases are denoted by Ⅰ-a(Ⅰ-b),Ⅱ,and Ⅲ,respectively.The three black solid lines represent the localization transition points determined by the analytical results.One can see that the analytical results match the numerical results.Moreover,we discuss that the relationship between the real-complex spectrum transition and the localization transition.It is found that the energy spectrum of the system can undergo two real-to-complex transitions.Specifically,during the transition from the fully extended phase to the intermediate phase,the first real-complex transition occurs,where part of the energy spectrum changes from the real spectrum to the complex spectrum,while another part spectrum remains real.When the system transitions from the intermediate phase to the fully localized phase,the energy spectrum completely transforms into a complex spectrum.These research results provide a reference for the study of localization transitio

关 键 词：非厄米 无序 耦合链 

分 类 号：O469[理学—凝聚态物理]