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Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-Andr\'{e} 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 quasi-periodic 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 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 as . The critical exponent of the inverse
participation ratio (IPR) for the th eigenstate is also determined as
. 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
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