Restoring Kibble-Zurek Scaling and Defect Freezing in Non-Hermitian Systems under Biorthogonal Framework

TL;DR

This paper develops a biorthogonal quantum framework to analyze nonadiabatic dynamics in non-Hermitian systems, revealing universal Kibble-Zurek scaling and defect freezing phenomena at exceptional points.

Contribution

It introduces a gauge-independent approach for nonadiabatic dynamics in non-Hermitian systems, clarifying defect scaling and freezing behaviors.

Findings

Defect production follows Kibble-Zurek power-law scaling at exceptional points.

Universal scaling behaviors are observed in the fast quench regime.

Defect freezing occurs when crossing the PT-broken region.

Abstract

Non-Hermitian physics provides an effective description of open and nonequilibrium systems and hosts many novel and intriguing phenomena such as exceptional points and non-Hermitian skin effect. Despite extensive theoretical and experimental studies, however, how to properly deal with the nonadiabatic dynamics in driven non-Hermitian quantum system is still under debate. Here, we develop a theoretical framework based on time-dependent biorthogonal quantum formalism by redefining the associated state to obtain the gauge-independent transition probability, and study the nonadiabatic dynamics of a linearly driven non-Hermitian system. In contrast to the normalization method that leads to a modified Kibble-Zurek scaling behavior, our approach predicts that the defect production at exceptional points exhibits power-law scaling behaviors conforming to the Kibble-Zurek mechanism. In the fast quench regime, universal scaling behaviors are also found with respect to the initial quenching parameter, which can be explained by the impulse-adiabatic approximation. Moreover, as trespassing the PT -broken region, the phenomenon of defect freezing, i.e., violation of adiabaticity, is observed.