Kibble−Zurek scaling of the dynamical localization−skin effect phase transition in a non-Hermitian quasi-periodic system under the open boundary condition

In the present study, the driven dynamics in a non-Hermitian Aubry–André (AA) model under the open boundary condition (OBC) are studied. For this model, non-Hermiticity is introduced by the non-reciprocal hopping, and this model undergoes a localization–skin effect phase transition depending on the strength of the quasi-periodic potential. Although the properties of non-Hermitian systems are very sensitive to the imposed boundary conditions, we find that the scaling behavior can also be described by the same set of the exponents under the periodic boundary condition (PBC). When the initial state is prepared deep in the localized phase and the potential strength is slowly driven through the critical point, we find that the driven dynamics of the localization length ξ and the inverse participation ratio (IPR) could be described by the Kibble–Zurek scaling (KZS). Then, we numerically verify these predictions for different initial states. Finally, the dynamical emergence of the skin effect state is found, and the dynamics can also be described by the Kibble−Zurek scaling with the same set of critical exponents.