Restoring Kibble-Zurek Scaling and Defect Freezing in Non-Hermitian Systems under Biorthogonal Framework
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arXiv
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| Format: | Preprint |
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2024
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| author | Deng, Menghua Li, Wei Hu, Kangyi Li, Fuxiang |
| author_facet | Deng, Menghua Li, Wei Hu, Kangyi Li, Fuxiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23633 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restoring Kibble-Zurek Scaling and Defect Freezing in Non-Hermitian Systems under Biorthogonal Framework Deng, Menghua Li, Wei Hu, Kangyi Li, Fuxiang Quantum Physics Other Condensed Matter 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. |
| title | Restoring Kibble-Zurek Scaling and Defect Freezing in Non-Hermitian Systems under Biorthogonal Framework |
| topic | Quantum Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2410.23633 |