Liouvillianity breaking in dissipative interacting Floquet systems under high-frequency drive

Periodically-driven (Floquet) systems have been attracted much interest as one of the most important class of nonequilibium systems. Floquet-Magnus (FM) expansion is a powerful tool for Floquet systems under high-frequency drives. In closed Floquet systems, it gives an effective static Hamiltonian which describes their stroboscopic dynamics. However, in dissipative Floquet systems dominated by a Liouvillian, it remains an important problem whether the FM expansion gives a static effective Liouvillian (Liouvillianity).

We have made an answer for generic systems with local interactions. We have found that, while noninteracting systems can either preserve or break Liouvillianity of the FM expansion, generic interacting systems always show its breaking (Liouvillianity breaking), and that Liouvillianity breaking in such systems is essentially caused by the spread of interactions in FM expansions. Our results imply that generic interacting dissipative Floquet systems under Markovianity do not have static Markovian counterparts in high-frequency regimes, giving a sign of emergent non-Markovianity.

Reference:
K. Mizuta, K. Takasan, and N. Kawakami, arXiv:2008.13104 (2020)