Constructing the Generalized Gibbs Ensemble after a Quantum Quench

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 postquench 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.