Universality classes of thermalization for mesoscopic Floquet systems

Abstract

We identify several phases of thermalization that describe regimes of behavior in isolated, periodically driven (Floquet), mesoscopic quantum chaotic systems. We also identify a new Floquet thermal ensemble -- the ladder ensemble -- that is qualitatively distinct from the featureless infinite-temperature state that is often assumed to describe the equilibrium of driven systems. The phases can be coarsely classified by (i) whether or not the system irreversibly exchanges energy of order $\omega$ with the drive, i.e., Floquet thermalizes, and (ii) the ensemble describing the final equilibrium in systems that do Floquet thermalize. These phases represent regimes of behavior in mesoscopic systems, but they are sharply defined in a large-system limit where the drive frequency $\omega$ scales up with system size $N$ as the $N\to\infty$ limit is taken: we examine frequency scalings ranging from a weak $\omega \sim \log N$, to stronger scalings ranging from $\omega \sim \sqrt{N}$ to $\omega \sim N$. We show that the transition where Floquet thermalization breaks down occurs at $\omega\sim N$ and, beyond that, systems that do not Floquet thermalize are distinguished based on the presence or absence of rare resonances across Floquet zones. We produce a thermalization phase diagram that is relevant for numerical studies of Floquet systems and experimental studies on small-scale quantum simulators, both of which lack a separation of scales between $N$ and $\omega$. A striking prediction of our work is that, under perfect isolation, certain realistic quench protocols from simple pure initial states can show Floquet thermalization to a novel type of Schrodinger-cat state that is a global superposition of states at distinct temperatures. Our work extends and organizes the theory of Floquet thermalization, heating, and equilibrium into the setting of mesoscopic quantum systems.