Two-step relaxation in local many-body Floquet systems

TL;DR

This paper investigates the relaxation dynamics of local many-body Floquet systems, revealing a two-phase exponential decay process with a critical time where the relaxation rate changes, challenging the simple exponential decay assumption.

Contribution

It demonstrates that relaxation in Floquet systems occurs in two phases with different rates and identifies a size-dependent critical time, extending the understanding beyond random circuits.

Findings

Relaxation proceeds in two exponential decay phases.

A critical time proportional to system size marks the rate change.

Phantom relaxation occurs beyond random circuit models.

Abstract

We want to understand how relaxation process from an initial non-generic state proceeds towards a long-time typical state reached under unitary quantum evolution. One would expect that after some initial correlation time relaxation will be a simple exponential decay with constant decay rate. We show that this is not necessarily the case. Studying various Floquet systems with fixed two-qubit gates, and focusing on purity and out-of-time-ordered correlation functions, we find that in many situations relaxation proceeds in two phases of exponential decay having different relaxation rates. Namely, in the thermodynamic limit the relaxation rate exhibits a change at a critical time proportional to system's size. The initial thermodynamically relevant rate can be slower or faster than the asymptotic one, demonstrating that the recently discovered phantom relaxation, in which the decay is slower than predicted by a nonzero transfer matrix gap, is not limited to only random circuits.