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

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Title: Pure real energy spectrum and exact anomalous mobility edges in a non-Hermitian flat band geometry.
Authors: Lu, Zhanpeng1 (AUTHOR), Liu, Hui2 (AUTHOR) liuhui99@sxu.edu.cn, Gu, Yan3 (AUTHOR) guyan@sxgkd.edu.cn, Xu, Zhihao2,4 (AUTHOR) xuzhihao@sxu.edu.cn
Source: Chinese Physics B. 2026, Vol. 35 Issue 7, p1-9. 9p.
Subjects: Skin effect, Lattice models (Statistical physics), Electric circuit design & construction, Metal-insulator transitions, Electronic band structure
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. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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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. [ABSTRACT FROM AUTHOR]
ISSN:16741056
DOI:10.1088/1674-1056/ae1efd