Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices

We study the combined effect of quasiperiodic disorder, driven, and interaction in periodically kicked Aubry-Andr\'e model. In noninteracting limit, by analyzing quasienergy spectrum statistics, we verify existence a dynamical localization transition high-frequency region, whereas statistics becomes intricate low-frequency region due to emergence extended/localized-to-multifractal edges spectrum, which separate multifractal states from extended (localized) states. When is introduced, find incommensurate potential can lead ergodic many-body-localization phase region. However, many-body vanishes even for strong disorder. Our studies demonstrate that model displays rich phenomena driving frequency plays an important role formation addition disorder strength.