Quantum quench in long-range field theories

TL;DR

This paper investigates how long-range quantum field theories equilibrate after a mass quench across different dimensions, highlighting the role of initial states and the non-local nature of conserved quantities.

Contribution

It provides a classification of equilibration regimes in long-range field theories and demonstrates the applicability of the Generalized Gibbs Ensemble in describing long-time correlations.

Findings

Equilibration depends on the dimension and initial state.

Long-time correlations are described by the Generalized Gibbs Ensemble when equilibration occurs.

All integrals of motion in the system are non-local.

Abstract

We study equilibration properties of observables in long-range field theories after the mass quench in $d=1,2$ and $3$ dimensions. We classify the regimes where we expect equilibration or its absence in different dimensions. In addition we study the effect of the initial state in the equilibration properties of our system. In the case of free field theories we show that whenever we have equilibration the long-time limit of correlations can be described by the Generalized Gibbs Ensemble. We prove that all integrals of motions in our system are non-local.