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

TL;DR

This study explores how long-range hopping in a non-Hermitian quasiperiodic model influences the non-Hermitian skin effect, revealing that extended hopping weakens the skin effect and affects the nature of eigenstates and spectra.

Contribution

It introduces a non-Hermitian Aubry-André-Harper model with power-law hoppings and shows how long-range interactions modify the skin effect and eigenstate properties.

Findings

Long-range hopping weakens the non-Hermitian skin effect.

Ergodic states have complex eigenvalues, multifractal states have real eigenvalues.

Both real and complex spectra can appear in the localized phase.

Abstract

In this paper, we investigate a non-Hermitian Aubry-Andr\'e-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.