Critical properties in the non-Hermitian Aubry-Andre-Stark model

TL;DR

This study investigates the critical properties of the localization transition in the non-Hermitian Aubry-Andre-Stark model, revealing new critical exponents and universality classes distinct from Hermitian models through finite-size scaling analysis.

Contribution

The paper introduces new critical exponents for the non-Hermitian AAS model and demonstrates their independence from nonreciprocal strength, establishing a different universality class from Hermitian models.

Findings

Identified two new sets of critical exponents for the non-Hermitian AAS model.

Showed that these exponents are independent of nonreciprocal strength.

Established a hybrid scaling function in the overlap region between critical phases.

Abstract

We explore the critical properties of the localization transition in the non-Hermitian Aubry-Andre-Stark (AAS) model with quasiperiodic and Stark potentials, where the non-Hermiticity comes from the nonreciprocal hopping. The localization length, the inverse participation ratio and the energy gap are adopted as the characteristic quantities. We perform the scaling analysis to derive the scaling functions of the three quantities with critical exponents in several critical regions, with respect to the quasiperiodic and Stark potentials and the nonreciprocal strength. We numerically verify the finite-size scaling forms and extract the critical exponents in different situations. Two groups of new critical exponents for the non-Hermitian AAS model and its pure Stark limit are obtained, which are distinct to those for the non-Hermitian Aubry-Andre model and their Hermitian counterparts. Our results indicate that the Hermitian and non-Hermitian AAS, Aubry-Andre, and Stark models belong to different universality classes. We demonstrate that these critical exponents are independent of the nonreciprocal strength, and remain the same in different critical regions and boundary conditions. Furthermore, we establish a hybrid scaling function with a hybrid exponent in the overlap region between the critical regions for the non-Hermitian AAS and Stark models.