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Exact mobility edges and topological phase transition in two-dimensional non-Hermitian quasicrystals

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Science China(Physics,Mechanics & Astronomy) 2022年第2期65卷 82-90页

作者： Zhi-Hao Xu Xu Xia Shu Chen Institute of Theoretical Physics and State Key Laboratory of Quantum Optics and Quantum Optics Devices Shanxi UniversityTaiyuan 030006China Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China Collaborative Innovation Center of Extreme Optics Shanxi UniversityTaiyuan 030006China Chern Institute of Mathematics and LPMC Nankai UniversityTianjin 300071China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China Yangtze River Delta Physics Research Center Liyang 213300China

The emergence of the mobility edge(ME)has been recognized as an important characteristic of Anderson localization.The difficulty in understanding the physics of the MEs in three-dimensional(3 D)systems from a microscopic image encourages the development of models in lower-dimensional systems that have exact MEs.While most of the previous studies are concerned with one-dimensional(1 D)quasiperiodic systems,the analytic results that allow for an accurate understanding of two-dimensional(2 D)cases are rare.In this work,we disclose an exactly solvable 2 D quasicrystal model with parity-time(PT)symmetry displaying exact MEs.In the thermodynamic limit,we unveil that the extended-localized transition point,observed at the PT symmetry breaking point,is topologically characterized by a hidden winding number defined in the dual space.The coupling waveguide platform can be used to realize the 2 D non-Hermitian quasicrystal model,and the excitation dynamics can be used to detect the localization features.

关键词： quasicrystals mobility edges non-Hermitian systems localization properties

mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

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Chinese Physics B 2021年第9期30卷 456-463页

作者：蒋相平乔艺曹俊鹏 Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China Songshan Lake Materials Laboratory Dongguan 523808China Peng Huanwu Center for Fundamental Theory Xi'an 710127China

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.

关键词： Anderson localization non-Hermitian quasiperiodic lattice mobility edges

mobility edges in one-dimensional finite-sized models with large quasi-periodic disorders

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Chinese Physics B 2023年第12期32卷 500-508页

作者：汤起芸贺言 College of Physics Sichuan UniversityChengdu 610064China

We study the one-dimensional tight-binding model with quasi-periodic disorders,where the quasi-period is tuned to be large compared to the system size.It is found that this type of model with large quasi-periodic disorders can also support the mobility edges,which is very similar to the models with slowly varying quasi-periodic disorders.The energy-matching method is employed to determine the locations of mobility edges in both types of models.These results of mobility edges are verified by numerical calculations in various examples.We also provide qualitative arguments to support the fact that large quasi-periodic disorders will lead to the existence of mobility edges.

关键词： quasi-periodic disorders mobility edges Aubry–Andre model