Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals

TL;DR

This paper introduces an analytical method to estimate mobility edges in non-Hermitian quasicrystals with broken duality, supported by numerical validation and applicable to models like NH Aubry-Andr{é}-Harper and GPD.

Contribution

It presents a new approximate analytical approach for locating mobility edges in a class of non-Hermitian quasicrystals that break duality, validated by numerical and limiting case comparisons.

Findings

Analytical solutions closely match numerical results.

Method accurately estimates mobility edges in NH quasicrystals.

Distinct dynamic behaviors observed in different regimes.

Abstract

We provide approximate solutions for the mobility edge (ME) that demarcates localized and extended states within a specific class of one-dimensional non-Hermitian (NH) quasicrystals. These NH quasicrystals exhibit a combination of nonreciprocal hopping terms and complex quasiperiodic on-site potentials. Our analytical approach is substantiated by rigorous numerical calculations, demonstrating significant accuracy. Furthermore, our ansatz closely agrees with the established limiting cases of the NH Aubry-Andr{\'e}-Harper (AAH) and Ganeshan-Pixley-Das Sarma (GPD) models, which have exact results, thereby enhancing its credibility. Additionally, we have examined their dynamic properties and discovered distinct behaviors in different regimes. Our research provides a practical methodology for estimating the position of MEs in a category of NH quasicrystals that break duality.