| Summary: | We analyze the dynamics of periodically driven (Floquet) Hamiltonians with short and long-range interactions, finding clear evidence for a thermalization time, τ^{*}, that increases exponentially with the drive frequency. 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 τ^{*}, the dynamics of the system is well approximated by evolution under a time-independent Hamiltonian, D_{eff}, for both short-range interacting systems, in agreement with recent rigorous bounds, as well as for long-range interacting systems, where such results do not exist at present.
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