Chaotic prethermal regimes and their time scales in nearly integrable many-body spin systems

Understanding the thermalization process in both classical and quantum many-body systems is a major open question in nonequilibrium many-body dynamics. In weakly nonintegrable models, thermalization is known to occur in two stages: the system first relaxes to a generalized statistical ensemble (GSE) while retaining memory of the conserved quantities associated with the integrable limit, and then the GSE melts to the true thermal state at a much later time. Through numerical studies, we discover several prethermal but chaotic regimes and show that the time scale associated with this melting process is asympotically longer than the time scale for the onset of chaos. Furthermore, we find that the melting time scale violates Fermi Golden Rule in a specific central spin model with XX interactions.