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

TL;DR

This paper investigates unique localization phenomena and mobility edges in non-Hermitian quasicrystals with disordered imaginary gauge fields, revealing anomalous transitions, spectral changes, and wave-packet dynamics.

Contribution

It introduces the concept of anomalous localization and mobility edges in non-Hermitian quasicrystals, highlighting new spectral and dynamical behaviors distinct from Hermitian systems.

Findings

Identifies an anomalous transition from a non-Hermitian skin effect phase to a localized phase.

Discovers an anomalous mobility edge separating localized states from macroscopic accumulation states.

Shows spectral winding and wave-packet dynamics reflect the anomalous localization structure.

Abstract

Localization in non-Hermitian quasicrystals can differ fundamentally from its Hermitian counterpart when non-reciprocity is spatially disordered. Here we study a one-dimensional non-Hermitian Aubry-Andr\'{e}-Harper chain with a Bernoulli imaginary gauge field and quasiperiodic onsite modulation. In the nearest-neighbor limit, we identify an anomalous transition from a fully erratic non-Hermitian skin effect (ENHSE) phase to a fully localized phase. Although the fractal dimension vanishes in both regimes, the Lyapunov exponent and the fluctuation of the eigenstate center of mass sharply distinguish them. For generic finite-size realizations, this transition is further accompanied by a complex-to-real spectral change under periodic boundary conditions and a change of spectral winding from nontrivial to trivial. With weak next-nearest-neighbor hopping, we uncover an anomalous mobility edge at the same location as in the Hermitian generalized Aubry-Andr\'{e}-Harper model, but separating Anderson-localized states from ENHSE-type macroscopic-accumulation states rather than extended states. We further show that this anomalous localization structure is reflected in spectral winding and wave-packet dynamics: single realizations exhibit winding-dependent drift, winding-resolved averaging preserves opposite directional responses, and full disorder averaging largely restores Hermitian-like transport. Our results establish practical diagnostics of anomalous localization and mobility edges in non-Hermitian quasicrystals.