Abstract
We study the dynamics of periodically-kicked many-body systems away from the high-frequency regime, and discuss a family 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 nonintegrable systems, and report on 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). Unlike the high-frequency regime, we find that the relevant heating times are model dependent: we analyze the stability of the prethermal plateau to small perturbations in the drive period, and show that, in a spin chain whose IFE is intractable, the plateau duration is insensitive to the perturbation strength, in contrast to a chain where the IFE admits the resummation of an entire subseries. Infinitesimal perturbations are enough to restore the ergodic properties of the system, and decrease 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 provide evidence that the evolved subsystem is described well by a thermal state w.r.t.~the IFE Hamiltonian, with a gradually changing temperature, in accord with the Eigenstate Thermalization Hypothesis.
Highlights
Periodic drives provide a versatile toolbox to investigate properties of quantum many-body systems [1,2,3,4,5]
in the unconstrained thermalization stage (III), we introduce a class of Floquet systems which later on allows us to extend the notion of Floquet prethermalization to intermediate and low drive frequencies
The inverse-frequency expansion (IFE) fails to predict the exact value of the energy density E ( ) in the “unconstrained thermalization” stage (III) of the dynamics, given E ( ) and Heff one can reconstruct the thermal state that characterizes the system at that point of time
Summary
Periodic drives provide a versatile toolbox to investigate properties of quantum many-body systems [1,2,3,4,5]. The physics in the prethermal plateau is well captured by the inverse-frequency expansion (IFE) [4] for the effective approximate local Hamiltonian Heff ≈ HF [49] This equilibrium-like regime facilitates significantly the analysis of Floquet systems. This is correlated with a progressively more nonlocal operator structure of the exact Floquet “Hamiltonian,” whose inverse-frequency approximation breaks down as an asymptotic series with the onset of infinite-temperature heating [48,72]. This has facilitated the study of prethermal transients in interacting topological models [79,80,81]
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