### ITAMP Fellow | Harvard University

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

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

Francisco Machado, Gregory D. Kahanamoku-Meyer, Dominic V. Else, Chetan Nayak, Norman Y. Yao
PR Research (2019)
arXiv:1708.01620

#### 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.