Stationary entanglement entropies following an interaction quench in 1D Bose gas

We analyze the entanglement properties of the asymptotic steady state after a quench from free to hard-core bosons in one dimension. The Renyi and on Neumann entanglement entropies are found to be extensive, and the latter coincides with the thermodynamic entropy of the generalized Gibbs ensemble (GCE). Computing the spectrum of the two-point function, we provide exact analytical results for both the leading extensive parts and the subleading terms for the entropies as well as for the cumutlants of the particle-number fluctuations. We also compare the extensive part of the entanglement entropy with the thermodynamic ones. showing that the GCE entropy equals the entanglement, one and it is twice the diagonal entropy.