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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 |
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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.
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Received: 17 April 2023
Revised: 25 June 2023
Accepted manuscript online: 05 July 2023
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PACS:
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72.15.Rn
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(Localization effects (Anderson or weak localization))
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72.20.Ee
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(Mobility edges; hopping transport)
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73.20.Fz
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(Weak or Anderson localization)
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| Fund: 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). |
Corresponding Authors:
Yanxia Liu, Li-Jun Lang
E-mail: yxliu-china@ynu.edu.cn;ljlang@scnu.edu.cn
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Cite this article:
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 2023 Chin. Phys. B 32 097204
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