Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains

TL;DR

This paper investigates the dynamics of periodically-kicked quantum spin chains at intermediate and low frequencies, revealing the formation of long-lived prethermal states and analyzing their stability and thermalization properties.

Contribution

It extends the concept of prethermalization beyond high-frequency regimes, providing numerical analysis of stability and thermalization in both integrable and nonintegrable spin chains.

Findings

Prethermal plateau formation at intermediate and low frequencies.

Plateau stability depends on the model and perturbation strength.

Subsystems thermalize with respect to the effective Hamiltonian.

Abstract

We study the dynamics of periodically-kicked many-body systems away from the high-frequency regime, and discuss a family of Floquet systems where the notion of prethermalization can be naturally extended to intermediate and low driving frequencies. We investigate numerically the dynamics of both integrable and nonintegrable systems, and report on the formation of a long-lived prethermal plateau, akin to the high-frequency limit, where the system thermalizes with respect to an effective Hamiltonian captured by the inverse-frequency expansion (IFE). Unlike the high-frequency regime, we find that the relevant heating times are model dependent: we analyze the stability of the prethermal plateau to small perturbations in the drive period, and show that, in a spin chain whose IFE is intractable, the plateau duration is insensitive to the perturbation strength, in contrast to a chain where the IFE admits the resummation of an entire subseries. Infinitesimal perturbations are enough to restore the ergodic properties of the system, and decrease residual finite-size effects. Although the regime where the Floquet system leaves the prethermal plateau and starts heating up to infinite temperature is not captured by the IFE, we provide evidence that the evolved subsystem is described well by a thermal state w.r.t.~the IFE Hamiltonian, with a gradually changing temperature, in accord with the Eigenstate Thermalization Hypothesis.