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We investigate a class of periodically driven many-body systems that allowsus to extend the phenomenon of prethermalization to the vicinity of isolatedintermediate-to-low drive frequencies away from the high-frequency limit. Weprovide numerical evidence for the formation of a parametrically long-livedprethermal plateau, captured by an effective Floquet Hamiltonian computed usingthe replica inverse-frequency expansion, and demonstrate its stabilityw.r.t.~random perturbations in the drive period. Considering exclusivelynonintegrable Floquet Hamiltonians, we find that heating rates arenon-universal: we observe Fermi's Golden Rule scaling, power-law scalinginconsistent with the Golden Rule, and non-power law scaling, depending on thedrive. Despite the asymptotic character of the inverse-frequency expansion, weshow that it describes the thermostatic properties of the state all along theevolution up to infinite temperature, with higher-order terms improving theaccuracy. Our results suggest a dynamical mechanism to gradually increasetemperature in isolated quantum simulators, such as ultracold atoms, and openup an alternative possibility to investigate thermal phase transitions and theinterplay between thermal and quantum criticality using Floquet drives.

Prethermalization and Thermalization in Periodically-Driven Many-Body Systems away from the High-Frequency Limit