Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons

TL;DR

This study investigates whether integrable many-body quantum systems relax to equilibrium, demonstrating through ab initio simulations that they do, and introducing a generalized ensemble that captures their long-term behavior more accurately than traditional thermodynamics.

Contribution

The paper provides the first ab initio numerical evidence of relaxation in integrable quantum systems and extends the Gibbs ensemble to account for conserved quantities.

Findings

Integrable systems can relax to a generalized equilibrium state.

The generalized ensemble predicts observable values after relaxation.

Memory of initial conditions persists longer than in non-integrable systems.

Abstract

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such state are. We confirm the relaxation hypothesis through a thorough ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which having already been observed in the recent experiment on the non-equilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita, T. Wenger, D. S. Weiss, Nature (London) 440, 900 (2006)].