Dynamical crossover behavior in the relaxation of quenched quantum many-body systems

A crossover between different power-law relaxation behaviors of many-body periodically driven integrable systems has come to light in recent years. We demonstrate, using integrable quantum systems, that similar kinds of dynamical transitions may also occur in the relaxation of such systems following a sudden quench. Particularly, we observe two distinct power-law relaxation behaviors following a sudden quench in the integrable XY model, depending upon whether the quenched Hamiltonian lies in the commensurate or the incommensurate phase. The relaxation behavior for quenches at and near the boundary line, called the disorder line (DL), separating these phases is also characterized. The relaxation at the DL shows a scaling exponent different from that for quenches to either of the commensurate or incommensurate phases. The transitions occur through a crossover from the commensurate or incommensurate scaling behavior to the DL scaling behavior. The crossover time diverges as a power law as the parameters of the final quenched Hamiltonian approach the DL. The transitions are also observed to be robust under weak integrability-breaking perturbations but disappear following strongly chaotic quenches.