# On Generalized Gibbs Ensembles with an infinite set of conserved charges

## TL;DR

This paper demonstrates that truncated Generalized Gibbs Ensembles (tGGE's) with finitely many conserved charges can accurately approximate steady states in integrable models like the XXZ chain, with increasing precision as more charges are included.

## Contribution

It introduces a new construction of tGGE's that can approximate steady states arbitrarily well and proposes a complete canonical ensemble based on a linear combination of charges.

## Key findings

- tGGE's can approximate steady states with arbitrary accuracy
- Numerical results show high precision with only 10-100 charges
- A new set of charges forms a complete canonical ensemble

## Abstract

We revisit the question of whether and how the steady states arising after non-equilibrium time evolution in integrable models (and in particular in the XXZ spin chain) can be described by the so-called Generalized Gibbs Ensemble (GGE). It is known that the micro-canonical ensemble built on a complete set of charges correctly describes the long-time limit of local observables, and recently a canonical ensemble was built by Ilievski et. al. using particle occupation number operators. Here we provide an alternative construction by considering truncated GGE's (tGGE's) that only include a finite number of well localized conserved operators. It is shown that the tGGE's can approximate the steady states with arbitrary precision, i.e. all physical observables are exactly reproduced in the infinite truncation limit. In addition, we show that a complete canonical ensemble can in fact be built in terms of a new (discrete) set of charges built as linear combinations of the standard ones. Our general arguments are applied to concrete quench situations in the XXZ chain, where the initial states are simple two-site or four-site product states. Depending on the quench we find that numerical results for the local correlators can be obtained with remarkable precision using truncated GGE's with only 10-100 charges.