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

TL;DR

This paper investigates how interactions in high-frequency driven dissipative systems cause breakdowns in Markovianity, revealing that generic many-body systems exhibit emergent non-Markovian behavior in Floquet dynamics.

Contribution

It demonstrates that in interacting Floquet-Lindblad systems, the FM expansion generally breaks Liouvillianity, indicating the absence of static Markovian descriptions at high frequencies.

Findings

Noninteracting systems can preserve or break Liouvillianity.

Generic many-body systems break Liouvillianity under finite drives.

Breakdown of Liouvillianity signals emergent non-Markovianity.

Abstract

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