Breakdown of Markovianity by interactions in stroboscopic Floquet-Lindblad dynamics under high-frequency drive

Floquet-Magnus (FM) expansion theory is a powerful tool in periodically driven (Floquet) systems under high-frequency drives. In closed systems, it dictates that their stroboscopic dynamics time-periodic Hamiltonian well captured by the FM expansion, which gives static effective Hamiltonian. On other hand, dissipative Liouvillian, remains an important and nontrivial problem whether Liouvillian describing continuous-time Markovian dynamics, we refer to as ``Liouvillianity'' of expansion. We answer this question for generic with local interactions. find while noninteracting can either break or preserve Liouvillianity few-body many-body interacting any finite drive, essentially caused propagation interactions via higher-order terms breaking implies Floquet regimes do not have (Markovian) counterparts, giving signature emergent non-Markovianity. Our provides useful insight quest unique phenomena systems.