Relaxation dynamics of integrable field theories after a global quantum quench

TL;DR

This paper investigates how local and semi-local observables in integrable quantum field theories relax after a global quench, revealing different decay behaviors and confirming findings in specific models.

Contribution

It demonstrates the fundamental difference in relaxation dynamics based on operator locality using linked cluster expansion and quench action methods.

Findings

Local operators exhibit exponential and power-law decay in relaxation.

Semi-local operators show only exponential decay.

Results confirmed in Ising, sinh-Gordon, and sine-Gordon models.

Abstract

We apply the linked cluster expansion as well as the quench action approach to study the time evolution of one-point functions after a quantum quench in integrable field theories. We argue that the relaxation towards the stationary value fundamentally differs depending on the locality properties of the considered observable: while for local operators both exponential and power-law decaying terms are present in the dynamics, for semi-local operators the latter are absent. We explicitly confirm this for the Ising field theory, the sinh-Gordon model, and the repulsive sine-Gordon model.