Generalized Gibbs Ensembles for Quantum Field Theories

TL;DR

This paper explores how non-local conservation laws influence the stationary states of quantum field theories after non-equilibrium dynamics, revealing the need for generalized Gibbs ensembles that incorporate these weaker forms of locality.

Contribution

It introduces the necessity of including non-(ultra-)local conservation laws in generalized Gibbs ensembles for accurate description of stationary states in QFTs.

Findings

Non-local conservation laws are essential for correct stationary state description.

Standard local conservation laws are insufficient in certain QFT scenarios.

Implications for integrable 1D quantum field theories are discussed.

Abstract

We consider the non-equilibrium dynamics in isolated systems, described by quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In a presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra-)local in the usual sense of QFT, but fulfil a significantly weaker form of locality. We discuss implications of our results for integrable QFTs in one spatial dimension.