Title: Exponentially Slow Heating in Short and Long-range Interacting Floquet Systems,
Abstract: We analyze the dynamics of periodically-driven (Floquet) Hamiltonians with
short- and long-range interactions, finding clear evidence for a thermalization
time, $\tau^*$, that increases exponentially with the drive frequency. We
observe this behavior, both in systems with short-ranged interactions, where
our results are consistent with rigorous bounds, and in systems with long-range
interactions, where such bounds do not exist at present. Using a combination of
heating and entanglement dynamics, we explicitly extract the effective energy
scale controlling the rate of thermalization. Finally, we demonstrate that for
times shorter than $\tau^*$, the dynamics of the system is well-approximated by
evolution under a time-independent Hamiltonian $D_{\mathrm{eff}}$, for both
short- and long-range interacting systems.