Anderson localization transition in a robust $\mathcal{PT}$-symmetric phase of a generalized Aubry-Andre model

TL;DR

This paper investigates a generalized Aubry-Andre model with $ ext{PT}$-symmetry, revealing a robust phase with real eigenvalues and an Anderson localization transition, enriching understanding of disorder effects in non-Hermitian systems.

Contribution

It introduces a $ ext{PT}$-symmetric generalized Aubry-Andre model exhibiting a stable phase with real eigenvalues and supports localization transitions, expanding the study of non-Hermitian disorder phenomena.

Findings

Existence of a robust $ ext{PT}$-symmetric phase with real eigenvalues

Observation of an Anderson localization transition within this phase

Complex phase diagram influenced by disorder and $ ext{PT}$-symmetry

Abstract

We study a generalized Aubry-Andre model that obeys $\mathcal{PT}$-symmetry. We observe a robust $\mathcal{PT}$-symmetric phase with respect to system size and disorder strength, where all eigenvalues are real despite the Hamiltonian being non-hermitian. This robust $\mathcal{PT}$-symmetric phase can support an Anderson localization transition, giving a rich phase diagram as a result of the interplay between disorder and $\mathcal{PT}$-symmetry. Our model provides a perfect platform to study disorder-driven localization phenomena in a $\mathcal{PT}$-symmetric system.