Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-Andr\'{e} model

TL;DR

This paper investigates the non-equilibrium dynamics of localization phase transitions in a non-Hermitian disordered Aubry-Andre9 model, establishing the applicability of Kibble-Zurek scaling and introducing hybrid scaling in complex localization regimes.

Contribution

It formulates and verifies Kibble-Zurek scaling for non-Hermitian localization transitions, including a hybrid version applicable to overlapping localization mechanisms.

Findings

Kibble-Zurek scaling applies to non-Hermitian localization dynamics.

Hybrid KZS is valid in the overlap of non-Hermitian and Anderson localization.

Critical exponents are consistent under open and periodic boundary conditions.

Abstract

The driven dynamics of localization transitions in a non-Hermitian Disordered Aubry-Andr\'{e} (DAA) model are examined under both open boundary conditions (OBC) and periodic boundary conditions (PBC). Through an analysis of the static properties of observables, including the localization length ($\xi$), inverse participation ratio ($\rm IPR$), and energy gap ($\Delta E$), we found that the critical exponents examined under PBC are also applicable under OBC. The Kibble-Zurek scaling (KZS) for the driven dynamics in the non-Hermitian DAA systems is formulated and numerically verified for different local-to-local quench directions. The hybrid KZS (HKZS) in the overlapping critical region of non-Hermitian DAA and Anderson localization is proposed and numerically confirmed the validity across a local-to-skin quench direction. This study generalizes the application of the KZS to the dynamical localization transitions within systems featuring dual localization mechanisms.