Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect

Abstract

In this paper, we investigate a non-Hermitian Aubry-André-Harper model characterized by power-law hoppings ($1/s^a$) and a quasi-periodic parameter $\beta$, where $a$ denotes the power-law index, $s$ represents the hopping distance, and $\beta$ belongs to the metallic mean family. In the intermediate phases, we find that ergodic states correspond to complex eigenvalues, multifractal states to real eigenvalues, and localized states may exhibit either complex or real eigenvalues. Moreover, both real and complex energy spectra emerge in the localized phase, with real spectra attributed to pseudo-Hermiticity. Under open boundary conditions, our analysis of fractal dimensions and eigenstates reveals that all ergodic states transform into skin states. Furthermore, we demonstrate that long-range hoppings weaken the skin effect, offering another perspective for exploring non-Hermitian skin effects.

11 pages, 8 figures

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Cited by in corpus (5)

• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Quantum-to-semiclassical Husimi dynamics of non-Hermitian localization transitions
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping