Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons

Abstract: We consider quantum quenches in the so-called $q$-boson lattice model. We argue that the Generalized Eigenstate Thermalization Hypothesis holds in this model, therefore the Generalized Gibbs Ensemble (GGE) gives a valid description of the stationary states in the long time limit. For a special class of initial states (which are the pure Fock states in the local basis) we are able to provide the GGE predictions for the resulting root densities. We also give predictions for the long-time limit of certain local operators. In the $q\to\infty$ limit the calculations simplify considerably, the wave functions are given by Schur polynomials and the overlaps with the initial states can be written as simple determinants. In two cases we prove rigorously that the GGE prediction for the root density is correct. Moreover, we calculate the exact time dependence of a physical observable (the one-site Emptiness Formation Probability) for the quench starting from the state with exactly one particle per site. In the long-time limit the GGE prediction is recovered.