Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

TL;DR

This study investigates how a one-dimensional Bose-Hubbard system relaxes and thermalizes after a sudden interaction quench from the atomic limit, using numerical methods to analyze steady states and ensemble equivalences.

Contribution

It provides a detailed numerical analysis of relaxation dynamics and thermalization in the 1D Bose-Hubbard model following a global interaction quench, connecting results to ensemble theories and recent experiments.

Findings

Relaxation occurs within a few tunneling times.

Stationary values match the diagonal ensemble predictions.

Canonical ensemble describes steady states well at small interactions.

Abstract

Motivated by recent experiments, we study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. Using exact diagonalization and the density matrix renormalization group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. Typically, the relaxation to stationary values occurs over just a few tunneling times. The stationary values are identical to the so-called diagonal ensemble on the system sizes accessible to our numerical methods and we further observe that the micro-canonical ensemble describes the steady state of many observables reasonably well for small and intermediate interaction strength. The expectation values of observables in the canonical ensemble agree quantitatively with the time averages obtained from the quench at small interaction strengths, and qualitatively provide a good description of steady-state values even in parameter regimes where the micro-canonical ensemble is not applicable due to finite-size effects. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis. Moreover, we also observe that the diagonal and the canonical ensemble are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Finally, we discuss implications of our results for the interpretation of a recent sudden expansion experiment [Phys. Rev. Lett. 110, 205301 (2013)], in which the same interaction quench was realized.