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Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-Andr\'{e} model
- Publication Year :
- 2022
-
Abstract
- 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.
- Subjects :
- Condensed Matter - Disordered Systems and Neural Networks
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2205.08271
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevB.106.014204