Universality classes of thermalization for mesoscopic Floquet systems

We identify several distinct phases of thermalization that can occur in Floquet, i.e., periodically driven, many-body quantum chaotic systems. These phases are representative of regimes of behavior in mesoscopic systems, but they are sharply defined in a particular large-system limit where the drive frequency $omega$ scales up with system size N as the usual large-N limit is taken. Thus, we produce a thermalization phase diagram that is relevant for numerical and experimental studies of finite Floquet systems. The phases can be coarsely classified by whether or not the system irreversibly exchanges energy of order $omega$ with the drive, i.e., Floquet thermalizes. Systems that do Floquet thermalize can be further classified based on the Floquet thermal ensemble that describes their final equilibrium, and we show that in most of the phase diagram where Floquet thermalization does occur, the final equilibrium is not a featureless ``infinite-temperature" state. We show that the transition where Floquet thermalization breaks down happens at an extensive drive frequency, and beyond that, further classification of systems that do not Floquet thermalize is based on the presence or absence of rare resonances. Our general theoretical arguments are supported with numerical simulations of a model system. We also simulate an experiment that can be realized on current quantum simulation platforms, that shows Floquet thermalization to a state that is a superposition of distinct temperatures.