Non-ergodic behaviour of clean Bose-Hubbard chains

TL;DR

This paper investigates ergodicity breaking in small, clean Bose-Hubbard chains, revealing a non-ergodic regime with volume-law entanglement that differs from many-body localization, and explores its dynamical signatures and potential persistence at larger sizes.

Contribution

It identifies a non-ergodic phase in the Bose-Hubbard chain distinct from many-body localization and analyzes its properties and dynamics.

Findings

Non-ergodic regime with volume-law entanglement entropy.

Ergodicity breaking not due to many-body localization.

Imbalance oscillations decay with increasing system size.

Abstract

We study ergodicity breaking in the clean Bose-Hubbard chain for small hopping strength. We see the existence of a non-ergodic regime by means of indicators as the half-chain entanglement entropy of the eigenstates, the average level spacing ratio, {the properties of the eigenstate-expectation distribution of the correlation and the scaling of the Inverse Participation Ratio averages.} We find that this ergodicity breaking {is different from many-body localization} because the average half-chain entanglement entropy of the eigenstates obeys volume law. This ergodicity breaking appears unrelated to the spectrum being organized in quasidegenerate multiplets at small hopping and finite system sizes, so in principle it can survive also for larger system sizes. We find that some imbalance oscillations in time which could mark the existence of a glassy behaviour in space are well described by the dynamics of a single symmetry-breaking doublet and {quantitatively} captured by a perturbative effective XXZ model. We show that the amplitude of these oscillations vanishes in the large-size limit. {Our findings are numerically obtained for systems with $L < 12$. Extrapolations of our scalings to larger system sizes should be taken with care, as discussed in the paper.