Marin Bukov (Sofia University, Bulgaria): Floquet (Pre-)thermalization in Many-Body Systems away from the High-Frequency Limit

We study the dynamics of periodically-driven many-body systems away from the high-frequency regime, and introduce a class of Floquet systems where the notion of prethermalization can be naturally extended to intermediate and low driving frequencies. We investigate numerically the dynamics of both integrable and non-integrable systems, and provide evidence for the formation of a long-lived prethermal plateau, akin to the high-frequency limit, where the system thermalizes with respect to an effective Hamiltonian captured by the inverse-frequency expansion (IFE). However, unlike the high-frequency regime, we find that heating rates can be both power-law or exponentially suppressed, depending on the properties of the drive Hamiltonian. We analyze the stability of the prethermal plateau to small perturbations in the periodic drive, and show that, for systems with power-law suppressed heating, the plateau duration is insensitive to the perturbation strength, in contrast to models with exponentially suppressed heating. Interestingly, any infinitesimal perturbation is enough to restore the ergodic properties of the system and eliminate residual finite-size effects. Although the regime where the Floquet system leaves the prethermal plateau and starts heating up to infinite temperature is not captured by the IFE, we find that the evolved subsystem is described well by a thermal state w.r.t. the IFE Hamiltonian, with a gradually changing temperature.