Dynamical localization and many-body localization in periodically kicked quasiperiodic lattices

We study the combined effect of quasiperiodic disorder, driven and interaction in the periodically kicked Aubry-André model. In the non-interacting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a dynamical localization transition in the high-frequency region, whereas we find the spectrum statistics becoming intricate with no abrupt transition occurring in the low-frequency region due to the emergence of the mobility edges in the quasienergy spectrum. When the interaction is introduced, we find the periodically kicked incommensurate potential can lead to a transition from ergodic to many-body-localization phase in the high-frequency region. However, the many-body localization phase vanishes in the low-frequency region even for strong quasiperiodic disorder. Our studies demonstrate that the periodically kicked Aubry-André model displays rich dynamical phenomena and the driving frequency plays an important role in the formation of manybody localization.