Onset of Floquet thermalization

In the presence of interactions, a closed, homogeneous (disorder-free) many-body system is believed to generically heat up to an infinite temperature ensemble when subjected to a periodic drive: in the spirit of the ergodicity hypothesis underpinning statistical mechanics, this happens as no energy or other conservation law prevents this. Here we present an interacting Ising chain driven by a field of time-dependent strength, where such heating begins only below a threshold value of the drive amplitude, above which the system exhibits nonergodic behavior. The onset appears at strong, but not fast driving. This in particular puts it beyond the scope of high-frequency expansions. The onset location shifts, but it is robustly present, across wide variations of the model Hamiltonian such as driving frequency and protocol, as well as the initial state. The portion of nonergodic states in the Floquet spectrum, while thermodynamically subdominant, has a finite entropy. We find that the magnetization as an emergent conserved quantity underpinning the freezing; indeed, the freezing effect is readily observed, as initially magnetized states remain partially frozen up to infinite time. This result, which resembles the Kolmogorov-Arnold-Moser theorem for classical dynamical systems, could be a valuable ingredient for extending Floquet engineering to the interacting realm.