Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories

TL;DR

This paper investigates the locality properties of the Generalized Gibbs Ensemble (GGE) in relativistic quantum field theories after a quench, highlighting the essential role of quasi-local charges in describing the steady state.

Contribution

It demonstrates that in continuous field theories, the GGE cannot be solely constructed from local charges and emphasizes the importance of quasi-local charges for an accurate description.

Findings

Existence of a sequence of truncated local GGEs converging to the steady state.

Quasi-local charges are necessary for an unambiguous GGE in continuum theories.

GGE is fully determined by expectation values of countable quasi-local charges.

Abstract

We study the quench dynamics in continuous relativistic quantum field theory, more specifically the locality properties of the large time stationary state. After a quantum quench in a one-dimensional integrable model, the expectation values of local observables are expected to relax to a Generalized Gibbs Ensemble (GGE), constructed out of the conserved charges of the model. Quenching to a free bosonic theory, it has been shown that the system indeed relaxes to a GGE described by the momentum mode occupation numbers. We first address the question whether the latter can be written directly in terms of local charges and we find that, in contrast to the lattice case, this is not possible in continuous field theories. We then investigate the less stringent requirement of the existence of a sequence of truncated local GGEs that converges to the correct steady state, in the sense of the expectation values of the local observables. While we show that such a sequence indeed exists, in order to unequivocally determine the so-defined GGE, we find that information about the expectation value of the recently discovered quasi-local charges is in the end necessary, the latter being the suitable generalization of the local charges while passing from the lattice to the continuum. Lastly, we study the locality properties of the GGE and show that the latter is completely determined by the knowledge of the expectation value of a countable set of suitably defined quasi-local charges.