Pre-thermalization in a non-integrable quantum spin chain after a quench

TL;DR

This paper investigates the non-equilibrium dynamics of a quantum Ising chain with long-range interactions, revealing the emergence of a pre-thermal state and analyzing its properties and eventual thermalization process.

Contribution

It introduces an exact mapping to a fully-connected bosonic lattice and develops a diagrammatic approach to study pre-thermalization and thermalization in non-integrable quantum spin chains.

Findings

Pre-thermal states emerge after a quench in the model.

Decay towards pre-thermal states and thermalization may be algebraic.

The diagrammatic approach aids in understanding the kinetic processes.

Abstract

We study the dynamics of a quantum Ising chain after the sudden introduction of a non-integrable long-range interaction. Via an exact mapping onto a fully-connected lattice of hard-core bosons, we show that a pre-thermal state emerges and we investigate its features by focusing on a class of physically relevant observables. In order to gain insight into the eventual thermalization, we outline a diagrammatic approach which complements the study of the previous quasi-stationary state and provides the basis for a self-consistent solution of the kinetic equation. This analysis suggests that both the temporal decay towards the pre-thermal state and the crossover to the eventual thermal one may occur algebraically.