Prethermalization and thermalization in models with weak integrability breaking

TL;DR

This paper investigates how weak integrability breaking affects the non-equilibrium dynamics of spinless fermion models, revealing persistent prethermalization states and their eventual drift to thermalization.

Contribution

It introduces a generalized equation of motion approach for weakly interacting systems and benchmarks it against DMRG, providing new insights into prethermalization and thermalization timescales.

Findings

Prethermalization plateaux are robust at weak integrability breaking.

Increasing integrability breaking causes a drift from prethermalization to thermalization.

A characteristic timescale for the crossover is identified.

Abstract

We study the effects of integrability breaking perturbations on the non-equilibrium evolution of many-particle quantum systems. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalizations of quantum Boltzmann equations. We benchmark our method against time dependent density matrix renormalization group computations and find it to be very accurate as long as interactions are weak. For small integrability breaking, we observe robust prethermalization plateaux for local observables on all accessible time scales. Increasing the strength of the integrability breaking term induces a "drift" away from the prethermalization plateaux towards thermal behaviour. We identify a time scale characterizing this cross-over.