Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model

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.