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

TL;DR

This paper investigates how periodically-driven quantum systems with short- and long-range interactions thermalize slowly, with a thermalization time that grows exponentially with drive frequency, and shows that their dynamics can be approximated by an effective static Hamiltonian before thermalization occurs.

Contribution

It demonstrates that the thermalization time in Floquet systems increases exponentially with drive frequency, extending understanding to both short- and long-range interactions, and identifies an effective Hamiltonian governing short-time dynamics.

Findings

Thermalization time $ au^*$ grows exponentially with drive frequency.

Short-time dynamics are well-described by an effective static Hamiltonian.

Results are consistent with rigorous bounds for short-range interactions.

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.