周期驱动非互易Aubry-André模型中的多重分形态和迁移率边  

Multifractal state and mobility edges in a periodically driven non-reciprocal Aubry-Andrémodel

作　　者：王宇佳 徐志浩 WANG Yujia;XU Zhihao(State Key Laboratory of Quantum Optics Technologies and Devices,Institute of Theoretical Physics,Shanxi University,Taiyuan 030006,China;Collaborative Innovation Center of Extreme Optics,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学理论物理研究所,光量子技术与器件全国重点实验室,太原030006 [2]山西大学,极端光学协同创新中心,太原030006

出　　处：《物理学报》2025年第9期311-318,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12375016);山西省基础研究计划(批准号:20210302123442);北京凝聚态物理国家实验室(批准号:2023BNLCMPKF001);山西省“1331工程”重点学科建设计划资助的课题.

摘　　要：研究了在非互易Aubry-André模型中由方波式周期驱动所诱导的多重分形态和迁移率边.通过数值计算逆参与率、能谱的实复转变以及平均逆参与率的标度分析等,发现在以高于临界频率的驱动下系统展现完全的局域相.同时在Floquet谱的特定区域存在CAT态,不同于厄米情况,其波函数分布的两个峰值展现非等权叠加的特性,这是由非互易物理所决定的.而以低于临界频率的驱动下,Floquet谱中存在迁移率边和多重分形态.该研究结果为周期驱动系统中局域化性质的研究提供了新的视角.In this work,we investigate the delocalization-localization transition of Floquet eigenstates in a driven chain with an incommensurate Aubry-André(AA)on-site potential and a small non-reciprocal hopping term that is driven periodically in time.The driving protocol is chosen such that the Floquet Hamiltonian corresponds to a localized phase in the high-frequency limit and a delocalized phase in the low-frequency limit.DqBy numerically calculating the inverse participation ratio and the fractal dimension,we identify a clearωc≈0.318πdelocalization-localization transition of the Floquet eigenstates at a critical frequency.This transition aligns with the real-to-complex spectrum transition of the Floquet Hamiltonian.For the drivenω>ωcfrequency,the system resides in a localized phase,and we observe the emergence of CAT states-linear superposition of localized single particle states-in the Floquet spectrum.These states exhibit weight distributions concentrated around a few nearby sites of the chain,forming two peaks of unequal weight due toω<ωcthe non-reciprocal effect,distinguishing them from the Hermitic case.In contrast,for,we identify the presence of a mobility edge over a range of driving frequencies,separating localized states(above the edge)from multifractal and extended states(below the edge).Notably,multifractal states are observed in the Floquet eigenspectrum across a broad frequency range.Importantly,we highlight that the non-driven,non-reciprocal AA model does not support multifractal states nor a mobility edge in its spectrum.Thus,our findings reveal unique dynamical signatures that do not exist in the non-driven non-Hermitian scenario,providing a fresh perspective on the localization properties of periodically driven systems.Finally,we provide a possible circuit experiment scheme for the periodically driven non-reciprocal AA model.In the following work,we will extend our research to clean systems,such as Stark models,to explore the influence of periodic driving on their localization properties.

关 键 词：周期驱动系统 局域化 迁移率边 非互易 

分 类 号：O415.5[理学—理论物理]