Entanglement detection in postquench nonequilibrium states: thermal Gibbs vs. generalized Gibbs ensemble

We use entanglement witnesses related to the entanglement negativity of the state to detect entanglement in the $XY$ chain in the postquench states in the thermodynamic limit after a quench when the parameters of the Hamiltonian are changed suddenly. The entanglement negativity is related to correlations, which in the postquench stationary state are described by a generalized Gibbs ensemble, in the ideal case. If, however, integrability breaking perturbations are present, the system is expected to thermalize. Here we compare the nearest-neighbor entanglement in the two circumstances.