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

• URL: http://arxiv.org/abs/2410.23633v1
• Date: Thu, 31 Oct 2024 05:01:00 GMT
• Title: Restoring Kibble-Zurek Scaling and Defect Freezing in Non-Hermitian Systems under Biorthogonal Framework
• Authors: Menghua Deng, Wei Li, Kangyi Hu, Fuxiang Li,
• Abstract summary: We develop a theoretical framework based on time-dependent biorthogonal quantum formalism. We study the nonadiabatic dynamics of a linearly driven non-Hermitian system.
• Score: 1.9460072625303615
• License:
• 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.

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