Onset of chaos and relaxation in isolated systems of interacting spins-1/2: energy shell approach

TL;DR

This paper investigates how chaos and relaxation emerge in isolated quantum spin-1/2 systems, showing that eigenstate delocalization within the energy shell predicts relaxation behavior regardless of integrability.

Contribution

It introduces an energy shell approach to identify chaos onset and demonstrates that relaxation dynamics are similar in both integrable and chaotic models, extending previous theories.

Findings

Relaxation occurs in both integrable and chaotic systems.

Eigenstate delocalization within the energy shell signals chaos onset.

Relaxation dynamics can be analytically described using two-body random interaction theory.

Abstract

We study the onset of chaos and statistical relaxation in two isolated dynamical quantum systems of interacting spins-1/2, one of which is integrable and the other chaotic. Our approach to identifying the emergence of chaos is based on the level of delocalization of the eigenstates with respect to the energy shell, the latter being determined by the interaction strength between particles or quasi-particles. We also discuss how the onset of chaos may be anticipated by a careful analysis of the Hamiltonian matrices, even before diagonalization. We find that despite differences between the two models, their relaxation process following a quench is very similar and can be described analytically with a theory previously developed for systems with two-body random interactions. Our results imply that global features of statistical relaxation depend on the degree of spread of the eigenstates within the energy shell and may happen to both integrable and non-integrable systems.