Breakdown of the generalized Gibbs ensemble for current-generating quenches

TL;DR

This paper explores the connection between relaxation to the generalized Gibbs ensemble (GGE) and dissipationless charge transport in integrable systems, demonstrating conditions for GGE formation and introducing an extended GGE for specific quenches.

Contribution

It establishes a link between GGE relaxation and charge stiffness saturation, and formulates an extended GGE including quasi-local conserved quantities for flux quenches.

Findings

GGE relaxation requires saturation of the Mazur bound by local conserved quantities.

A non-GGE steady state with current can be generated in a 1D interacting fermion model.

An extended GGE with quasi-local conserved quantities can describe certain non-equilibrium states.

Abstract

We establish a relation between two hallmarks of integrable systems: the relaxation towards the generalized Gibbs ensemble (GGE) and the dissipationless charge transport. We show that the former one is possible only if the so called Mazur bound on the charge stiffness is saturated by local conserved quantities. As an example we show how a non--GGE steady state with a current can be generated in the one-dimensional model of interacting spinless fermions with a flux quench. Moreover an extended GGE involving the quasi-local conserved quantities can be formulated for this case.