Anomalous Localization and Mobility Edges in Non-Hermitian Quasicrystals with Disordered Imaginary Gauge Fields

• URL: http://arxiv.org/abs/2601.14754v1
• Date: Wed, 21 Jan 2026 08:14:27 GMT
• Title: Anomalous Localization and Mobility Edges in Non-Hermitian Quasicrystals with Disordered Imaginary Gauge Fields
• Authors: Guolin Nan, Zhijian Li, Feng Mei, Zhihao Xu,
• Abstract summary: We study anomalous localization in a one-dimensional non-Hermitian quasicrystal with a spatially disordered imaginary gauge field.<n>We show that the fractal dimension cannot distinguish these phases, whereas the Lyapunov exponent and center-of-mass fluctuations provide sharp diagnostics.
• Score: 3.357660889571676
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study anomalous localization in a one-dimensional non-Hermitian quasicrystal with a spatially disordered imaginary gauge field. The system is a generalized Aubry-André-Harper (AAH) chain with asymmetric nearest- and next-nearest-neighbor hoppings generated by a Bernoulli imaginary gauge field and a quasiperiodic onsite potential. In the standard non-Hermitian AAH limit, the system undergoes a transition from a fully erratic non-Hermitian skin effect (ENHSE) phase to a fully localized phase. We show that the fractal dimension cannot distinguish these phases, whereas the Lyapunov exponent and center-of-mass fluctuations provide sharp diagnostics. This transition is accompanied by a complex-to-real spectral change under periodic boundary conditions and a topological change of the spectral winding number. With next-nearest-neighbor hopping, we uncover an anomalous mobility edge separating Anderson-localized states from ENHSE states, rather than extended states. This mobility edge is captured by an energy-dependent winding number that vanishes in the localized regime. Finally, we propose a dynamical probe based on wave-packet expansion: for typical disorder realizations, the dynamics shows winding-controlled drift and disorder-selected pinning or boundary-wrapping recurrence, while disorder averaging restores Hermitian-like transport. These results offer practical spectral, topological, and dynamical diagnostics of anomalous localization and mobility edges in non-Hermitian quasicrystals.

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