General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents

doi:10.1088/1674-1056/ace426

中国物理B ›› 2023, Vol. 32 ›› Issue (9): 97204-097204.doi: 10.1088/1674-1056/ace426

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents

Sheng-Lian Jiang(蒋盛莲)¹, Yanxia Liu(刘彦霞)^2,†, and Li-Jun Lang(郎利君)^1,3,‡

1 School of Physics, South China Normal University, Guangzhou 510006, China;
2 School of Physics and Astronomy, Yunnan University, Kunming 650091, China;
3 Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics, South China Normal University, Guangzhou 510006, China

收稿日期:2023-04-17 修回日期:2023-06-25 接受日期:2023-07-05 出版日期:2023-08-15 发布日期:2023-09-07
通讯作者: Yanxia Liu, Li-Jun Lang E-mail:yxliu-china@ynu.edu.cn;ljlang@scnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 12204406), the National Key Research and Development Program of China (Grant No. 2022YFA1405304), and the Guangdong Provincial Key Laboratory (Grant No. 2020B1212060066).

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents

Sheng-Lian Jiang(蒋盛莲)¹, Yanxia Liu(刘彦霞)^2,†, and Li-Jun Lang(郎利君)^1,3,‡

1 School of Physics, South China Normal University, Guangzhou 510006, China;
2 School of Physics and Astronomy, Yunnan University, Kunming 650091, China;
3 Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics, South China Normal University, Guangzhou 510006, China

Received:2023-04-17 Revised:2023-06-25 Accepted:2023-07-05 Online:2023-08-15 Published:2023-09-07
Contact: Yanxia Liu, Li-Jun Lang E-mail:yxliu-china@ynu.edu.cn;ljlang@scnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 12204406), the National Key Research and Development Program of China (Grant No. 2022YFA1405304), and the Guangdong Provincial Key Laboratory (Grant No. 2020B1212060066).

摘要/Abstract

摘要： We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts. This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved. To demonstrate the validity of this mapping, we apply it to two non-Hermitian localization models: an Aubry-André-like model with nonreciprocal hopping and complex quasiperiodic potentials, and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping. We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models. This general mapping may catalyze further studies on mobility edges, Lyapunov exponents, and other significant quantities pertaining to localization in non-Hermitian mosaic models.

关键词: non-Hermitian mosaic model, mosaic-to-non-mosaic mapping, mobility edge, Lyapunov exponent

Abstract: We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts. This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved. To demonstrate the validity of this mapping, we apply it to two non-Hermitian localization models: an Aubry-André-like model with nonreciprocal hopping and complex quasiperiodic potentials, and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping. We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models. This general mapping may catalyze further studies on mobility edges, Lyapunov exponents, and other significant quantities pertaining to localization in non-Hermitian mosaic models.

Key words: non-Hermitian mosaic model, mosaic-to-non-mosaic mapping, mobility edge, Lyapunov exponent

中图分类号: (Localization effects (Anderson or weak localization))

72.15.Rn

72.20.Ee (Mobility edges; hopping transport) 73.20.Fz (Weak or Anderson localization)

Sheng-Lian Jiang(蒋盛莲), Yanxia Liu(刘彦霞), and Li-Jun Lang(郎利君). General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents[J]. 中国物理B, 2023, 32(9): 97204-097204.

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General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents

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