Dynamical localization-delocalization crossover in the Aubry-André-Harper model

Examining the Aubry-Andr\'e-Harper (AAH) model driven by periodic fields, we find a crossover between the localization and delocalization phases. This is different from the sharp phase boundary in the AAH model without drives. On the contrary, the phase boundary in the present model depends on the frequency and amplitude of the driving field. We show numerically the dependence of the phase boundary on the frequency and amplitude and reveal the physics behind the relationship. The effect of aperiodicity of the drive on the localization-delocalization crossover is also investigated by numerical simulations. The results may be useful for engineering novel phases in periodically driven systems.