Pure real energy spectrum and exact anomalous mobility edges in a non-Hermitian flat band geometry

doi:10.1088/1674-1056/ae1efd

中国物理B ›› 2026, Vol. 35 ›› Issue (7): 77101-077101.doi: 10.1088/1674-1056/ae1efd

• • 上一篇

Pure real energy spectrum and exact anomalous mobility edges in a non-Hermitian flat band geometry

Zhanpeng Lu(陆展鹏)¹, Hui Liu(刘辉)^2,†, Yan Gu(古燕)^3,‡, and Zhihao Xu(徐志浩)^2,4,§

1 Department of Physics, XinZhou Normal University, Xinzhou 034000, China;
2 Institute of Theoretical Physics and State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University, Taiyuan 030006, China;
3 Shanxi Vocational University of Engineering Science and Technology, Jinzhong 030619, China;
4 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

收稿日期:2025-08-20 修回日期:2025-11-07 接受日期:2025-11-13 发布日期:2026-07-02
通讯作者: Hui Liu, Yan Gu, Zhihao Xu E-mail:liuhui99@sxu.edu.cn;guyan@sxgkd.edu.cn;xuzhihao@sxu.edu.cn
基金资助:
This work is supported by the National Natural Science Foundation of China (Grant Nos. 12375016 and 12461160324), Beijing National Laboratory for Condensed Matter Physics (Grant No. 2023BNLCMPKF001), and the Fundamental Research Program of Shanxi Province (Grant No. 202403021212025).

Pure real energy spectrum and exact anomalous mobility edges in a non-Hermitian flat band geometry

Zhanpeng Lu(陆展鹏)¹, Hui Liu(刘辉)^2,†, Yan Gu(古燕)^3,‡, and Zhihao Xu(徐志浩)^2,4,§

1 Department of Physics, XinZhou Normal University, Xinzhou 034000, China;
2 Institute of Theoretical Physics and State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University, Taiyuan 030006, China;
3 Shanxi Vocational University of Engineering Science and Technology, Jinzhong 030619, China;
4 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

Received:2025-08-20 Revised:2025-11-07 Accepted:2025-11-13 Published:2026-07-02
Contact: Hui Liu, Yan Gu, Zhihao Xu E-mail:liuhui99@sxu.edu.cn;guyan@sxgkd.edu.cn;xuzhihao@sxu.edu.cn
Supported by:
This work is supported by the National Natural Science Foundation of China (Grant Nos. 12375016 and 12461160324), Beijing National Laboratory for Condensed Matter Physics (Grant No. 2023BNLCMPKF001), and the Fundamental Research Program of Shanxi Province (Grant No. 202403021212025).

摘要/Abstract

摘要： The interplay between quasi-periodicity and non-Hermiticity can give rise to rich localization phenomena. In this work, we investigate the localization transition in a one-dimensional nonreciprocal cross-stitch flat band lattice with diagonal quasi-periodic mosaic modulation, which incorporates both constant and quasi-periodic potentials. In general, non-reciprocity induces the skin effect in non-Hermitian systems through nonreciprocal transitions. However, in this work, we find that in a non-reciprocal flat band lattice, when the constant potential is zero, the skin effect does not exist in the system, and the energy spectrum remains purely real and well-defined. In the presence of a non-zero constant potential, we derive analytical solutions for a class of anomalous mobility edges (AMEs) under periodic boundary conditions (PBCs), revealing the systems localization and critical properties. Through analytic results, we demonstrate that the system is fundamentally equivalent to a generalized non-Hermitian Aubry—André (AA) model. Importantly, this equivalence implies the existence of a transition from a critical phase to a localized phase, as predicted by the non-Hermitian AA model. However, our analysis reveals that the transition point from the critical phase to the localized phase is energy-dependent, which fundamentally accounts for the emergence of AMEs. Furthermore, we design a classical electrical circuit to experimentally realize our system. This work provides new insights into localization transitions in non-Hermitian flat band systems.

关键词: non-Hermiticity, localization transition, quasi-periodic potentials

Abstract: The interplay between quasi-periodicity and non-Hermiticity can give rise to rich localization phenomena. In this work, we investigate the localization transition in a one-dimensional nonreciprocal cross-stitch flat band lattice with diagonal quasi-periodic mosaic modulation, which incorporates both constant and quasi-periodic potentials. In general, non-reciprocity induces the skin effect in non-Hermitian systems through nonreciprocal transitions. However, in this work, we find that in a non-reciprocal flat band lattice, when the constant potential is zero, the skin effect does not exist in the system, and the energy spectrum remains purely real and well-defined. In the presence of a non-zero constant potential, we derive analytical solutions for a class of anomalous mobility edges (AMEs) under periodic boundary conditions (PBCs), revealing the systems localization and critical properties. Through analytic results, we demonstrate that the system is fundamentally equivalent to a generalized non-Hermitian Aubry—André (AA) model. Importantly, this equivalence implies the existence of a transition from a critical phase to a localized phase, as predicted by the non-Hermitian AA model. However, our analysis reveals that the transition point from the critical phase to the localized phase is energy-dependent, which fundamentally accounts for the emergence of AMEs. Furthermore, we design a classical electrical circuit to experimentally realize our system. This work provides new insights into localization transitions in non-Hermitian flat band systems.

Key words: non-Hermiticity, localization transition, quasi-periodic potentials

中图分类号: (Lattice fermion models (Hubbard model, etc.))

71.10.Fd

71.23.An (Theories and models; localized states) 61.44.Br (Quasicrystals)

Zhanpeng Lu(陆展鹏), Hui Liu(刘辉), Yan Gu(古燕), and Zhihao Xu(徐志浩). Pure real energy spectrum and exact anomalous mobility edges in a non-Hermitian flat band geometry[J]. 中国物理B, 2026, 35(7): 77101-077101.

Zhanpeng Lu(陆展鹏), Hui Liu(刘辉), Yan Gu(古燕), and Zhihao Xu(徐志浩). Pure real energy spectrum and exact anomalous mobility edges in a non-Hermitian flat band geometry[J]. Chin. Phys. B, 2026, 35(7): 77101-077101.

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Pure real energy spectrum and exact anomalous mobility edges in a non-Hermitian flat band geometry

Pure real energy spectrum and exact anomalous mobility edges in a non-Hermitian flat band geometry

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