Exponentially Slow Heating in Short and Long-range Interacting Floquet Systems

Understand

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.