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

TL;DR

This paper investigates dynamical crossover behaviors in the relaxation of quenched integrable quantum systems, revealing phase-dependent power-law relaxations, a novel scaling at the disorder line, and robustness under weak perturbations.

Contribution

It demonstrates the existence of dynamical transitions and crossover behaviors in the relaxation of quenched integrable systems, including a new scaling exponent at the disorder line.

Findings

Two distinct power-law relaxation behaviors depending on the phase

A new scaling exponent at the disorder line

Crossover time diverges as parameters approach the disorder line

Abstract

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 new scaling exponent previously unexplored. The transitions occur through a crossover from the commensurate/incommensurate scaling behavior to the DL scaling behavior. The crossover time diverges like 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.