Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model

TL;DR

This paper develops a method to construct complete bases of conserved charges with varying locality in the Lieb-Liniger model, enabling better description of quantum quenches and initial states, with potential applications to all integrable models.

Contribution

It introduces a general procedure for constructing complete bases of conserved charges with different locality properties in the Lieb-Liniger model, applicable to all integrable systems.

Findings

Constructed bases of charges with finite expectation values for arbitrary initial states.

Applied these charges to analyze quantum quenches in the Lieb-Liniger model.

Demonstrated the generality of the charge construction method for integrable models.

Abstract

We consider the construction of a generalized Gibbs ensemble composed of complete bases of conserved charges in the repulsive Lieb-Liniger model. We will show that it is possible to construct these bases with varying locality as well as demonstrating that such constructions are always possible provided one has in hand at least one complete basis set of charges. This procedure enables the construction of bases of charges that possess well defined, finite expectation values given an arbitrary initial state. We demonstrate the use of these charges in the context of two different quantum quenches: a quench where the strength of the interactions in a one-dimensional gas is switched suddenly from zero to some finite value and the release of a one dimensional cold atomic gas from a confining parabolic trap. While we focus on the Lieb-Liniger model in this paper, the principle of the construction of these charges applies to all integrable models, both in continuum and lattice form.