Thermalization in an interacting spin system in the transition from integrability to chaos

A stringent analysis of nonequilibrium dynamics and thermalization in a complex interacting spin system, which transits from integrability to chaos, is performed. The applicability of both standard thermodynamical ensembles-canonical and microcanonical and the generalized Gibbs ensemble is tested. The role of constants of motion is studied, and a critical analysis of the usual definition of quantum integrability is performed. Different possible thermalization mechanisms are also analyzed. We find significant discrepancies between the time averages of some observables and the prediction from the thermodynamical ensembles within the ergodic region, so we conclude that quantum chaos does not guarantee thermalization. We also find that quantum integrable dynamics keeps more memory concerning the initial state, which is in part stored in a set of constants of motion that can be explicitly obtained.