An exact formalism for the quench dynamics of integrable models

TL;DR

This paper introduces an exact formalism to analyze the quench dynamics of integrable models, specifically applying it to the Lieb-Liniger model, revealing how the system evolves towards different asymptotic states depending on the interaction strength.

Contribution

The paper generalizes Yudson's approach to study the quench dynamics of the Lieb-Liniger model, providing a new exact method for arbitrary initial states and analyzing long-term behavior.

Findings

Repulsive interactions lead to a strongly repulsive gas asymptote.

Attractive interactions result in a dominant maximal bound state.

The system equilibrates without thermalizing, differing from non-integrable systems.

Abstract

We describe a formulation for studying the quench dynamics of integrable systems generalizing an approach by Yudson. We study the evolution of the Lieb-Liniger model, a gas of interacting bosons moving on the continuous infinite line and interacting via a short range potential. The formalism allows us to quench the system from any initial state. We find that for any value of repulsive coupling independently of the initial state the system asymptotes towards a strongly repulsive gas, while for any value of attractive coupling, the system forms a maximal bound state that dominates at longer times. In either case the system equilibrates but does not thermalize. We compare this to quenches in a Bose-Hubbard lattice and show that there, initial states determine long-time dynamics independent of the sign of the coupling.