Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model

• URL: http://arxiv.org/abs/2108.07178v3
• Date: Wed, 12 Jan 2022 13:21:35 GMT
• Title: Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Authors: Longwen Zhou and Yongjian Gu
• Abstract summary: Non-Hermitian effects could trigger spectrum, localization and topological phase transitions in quasiperiodic lattices. We propose a non-Hermitian extension of the Maryland model, which forms a paradigm in the study of localization and quantum chaos. Explicit expressions of the complex energy dispersions, phase boundaries and mobility edges are found.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Non-Hermitian effects could trigger spectrum, localization and topological phase transitions in quasiperiodic lattices. We propose a non-Hermitian extension of the Maryland model, which forms a paradigm in the study of localization and quantum chaos by introducing asymmetry to its hopping amplitudes. The resulting nonreciprocal Maryland model is found to possess a real-to-complex spectrum transition at a finite amount of hopping asymmetry, through which it changes from a localized phase to a mobility edge phase. Explicit expressions of the complex energy dispersions, phase boundaries and mobility edges are found. A topological winding number is further introduced to characterize the transition between different phases. Our work introduces a unique type of non-Hermitian quasicrystal, which admits exactly obtainable phase diagrams, mobility edges, and holding no extended phases at finite nonreciprocity in the thermodynamic limit.

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