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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 quasiperiodic potential, this model undergoes a localization-delocalization phase transition. We find that the localization length satisfies ^- with being the distance from the critical point and =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 for the nth eigenstate is also determined as s=0. 1197. By changing 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.
Zhai et al. (Fri,) studied this question.