Real-complex transition driven by quasiperiodicity: a new universality class beyond $\mathcal{PT}$ symmetric one

TL;DR

This paper uncovers a new universality class of real-complex spectral transition in non-Hermitian quasiperiodic lattice models, extending beyond the traditional $ ext{PT}$ symmetric framework, through analytical duality and spectral analysis.

Contribution

It introduces a dual mapping relation in non-Hermitian quasiperiodic systems and rigorously demonstrates a novel real-complex transition outside the $ ext{PT}$ symmetric class.

Findings

Existence of a dual mapping between different potential regimes.

Analytical expression for the mobility edge in the model.

Identification of a new universality class of spectral transition.

Abstract

We study a one-dimensional lattice model subject to non-Hermitian quasiperiodic potentials. Firstly, we strictly demonstrate that there exists an interesting dual mapping relation between $|a|<1$ and $|a|>1$ with regard to the potential tuning parameter $a$. The localization property of $|a|<1$ can be directly mapping to that of $|a|>1$, the analytical expression of the mobility edge of $|a|>1$ is therefore obtained through spectral properties of $|a|<1$. More impressive, we prove rigorously that even if the phase $\theta \neq 0$ in quasiperiodic potentials, the model becomes non-$\mathcal{PT}$ symmetric, however, there still exists a new type of real-complex transition driven by non-Hermitian disorder, which is a new universality class beyond $\mathcal{PT}$ symmetric class.