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We study the dynamics of periodically-kicked many-body systems away from thehigh-frequency regime, and discuss a family of Floquet systems where the notionof prethermalization can be naturally extended to intermediate and low drivingfrequencies. We investigate numerically the dynamics of both integrable andnonintegrable systems, and report on the formation of a long-lived prethermalplateau, akin to the high-frequency limit, where the system thermalizes withrespect to an effective Hamiltonian captured by the inverse-frequency expansion(IFE). Unlike the high-frequency regime, we find that the relevant heatingtimes are model dependent: we analyze the stability of the prethermal plateauto small perturbations in the drive period, and show that, in a spin chainwhose IFE is intractable, the plateau duration is insensitive to theperturbation strength, in contrast to a chain where the IFE admits theresummation of an entire subseries. Infinitesimal perturbations are enough torestore the ergodic properties of the system, and decrease residual finite-sizeeffects. Although the regime where the Floquet system leaves the prethermalplateau and starts heating up to infinite temperature is not captured by theIFE, we provide evidence that the evolved subsystem is described well by athermal state w.r.t.~the IFE Hamiltonian, with a gradually changingtemperature, in accord with the Eigenstate Thermalization Hypothesis.

Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains