Constructing the generalized Gibbs ensemble after a quantum quench

TL;DR

This paper develops a numerical method to study the long-term out-of-equilibrium dynamics of a 1D Bose gas after a quantum quench and constructs the generalized Gibbs ensemble for integrable models, comparing predictions with observed dynamics.

Contribution

It introduces a numerical renormalization group approach for the Lieb-Liniger model and provides a general construction of the generalized Gibbs ensemble for integrable systems.

Findings

The method tracks dynamics to infinite time.

The generalized Gibbs ensemble accurately predicts long-term behavior.

Comparison shows good agreement between theory and simulation.

Abstract

Using a numerical renormalization group based on exploiting an underlying exactly solvable non- relativistic theory, we study the out-of-equilibrium dynamics of a 1D Bose gas (as described by the Lieb-Liniger model) released from a parabolic trap. Our method allows us to track the post-quench dynamics of the gas all the way to infinite time. We also exhibit a general construction, applicable to all integrable models, of the thermodynamic ensemble that has been suggested to govern this dynamics, the generalized Gibbs ensemble. We compare the predictions of equilibration from this ensemble against the long time dynamics observed using our method.