Solution for an interaction quench in the Lieb-Liniger Bose gas

TL;DR

This paper analyzes a quantum quench in the Lieb-Liniger Bose gas, deriving the exact non-thermal steady state using a variational method, highlighting a case where the generalized Gibbs ensemble fails.

Contribution

It provides the first thermodynamically exact solution to an interacting quench in the Lieb-Liniger model using a novel variational approach.

Findings

Exact non-thermal steady state obtained

Naive GGE implementation fails in this scenario

Highlights the importance of variational methods for interacting quenches

Abstract

We study a quench protocol where the ground state of a free many-particle bosonic theory in one dimension is let unitarily evolve in time under the integrable Lieb-Liniger Hamiltonian of $\delta$-interacting repulsive bosons. By using a recently-proposed variational method, we here obtain the exact non-thermal steady-state of the system in the thermodynamic limit, and discuss some of its main physical properties. Besides being a rare case of a thermodynamically exact solution to a truly interacting quench situation, this interestingly represents an example where a naive implementation of the generalized Gibbs ensemble fails.