| Autor: |
Zhai, Liang-Jun, Huang, Guang-Yao, Yin, Shuai |
| Rok vydání: |
2022 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| DOI: |
10.1103/PhysRevB.106.014204 |
| Popis: |
In this paper, we investigate the driven dynamics of the localization transition in the non-Hermitian Aubry-Andr\'{e} model with the periodic boundary condition. Depending on the strength of the quasi-periodic potential $\lambda$, this model undergoes a localization-delocalization phase transition. We find that the localization length $\xi$ satisfies $\xi\sim \varepsilon^{-\nu}$ with $\varepsilon$ being the distance from the critical point and $\nu=1$ being a universal critical exponent independent of the non-Hermitian parameter. In addition, from the finite-size scaling of the energy gap between the ground state and the first excited state, we determine the dynamic exponent $z$ as $z=2$. The critical exponent of the inverse participation ratio (IPR) for the $n$th eigenstate is also determined as $s=0.1197$. By changing $\varepsilon$ linearly to cross the critical point, we find that the driven dynamics can be described by the Kibble-Zurek scaling (KZS). Moreover, we show that the KZS with the same set of the exponents can be generalized to the localization phase transitions in the excited states. |
| Databáze: |
arXiv |
| Externí odkaz: |
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