Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems

TL;DR

This paper investigates how quasiperiodic potentials induce localization and fractal structures in non-Hermitian systems, revealing mobility edges, self-similarity, and the effects of longer-range hopping on topological and localization properties.

Contribution

It demonstrates the existence of a critical potential strength for localization in non-Hermitian quasiperiodic systems, including the effects of longer-range hopping and the emergence of mobility edges and self-similar eigenvalue structures.

Findings

Identification of a critical potential strength increasing linearly with antisymmetric hopping

Emergence of mobility edges due to longer-range hopping

Observation of self-similar structures in eigenvalue ratios and other quantities

Abstract

We analyze the localization behavior in a non-Hermitian system subject to a quasiperiodic onsite potential. We characterize localization transitions using multiple quantitative indicators, including inverse participation ratio (IPR), eigenstate fractal dimension (EFD), extended eigenstate ratio (EER), and spectral survival ratio. Despite the breaking of self-dual symmetry due to non-Hermiticity, our results reveal the existence of a critical potential strength, with its value increasing linearly with the nearest-neighbor antisymmetric hopping term. On the other hand, the inclusion of longer-range hopping not only enriches the topological properties but also gives rise to novel localization phenomena. In particular, it induces the emergence of mobility edges, as evidenced by both IPR and EFD, along with distinct features in the spectrum fractal dimension, which we extract using the box-counting method applied to the complex energy spectrum. Additionally, we uncover self-similar structures in various quantities, such as EER and complex eigenvalue ratio, as the potential strength varies. These findings highlight important aspects of localization and fractal phenomena in non-Hermitian quasiperiodic systems.