Observation of slow relaxation due to Hilbert space fragmentation in strongly interacting Bose-Hubbard chains

TL;DR

This study experimentally observes slow relaxation in a strongly interacting Bose-Hubbard chain, attributing it to Hilbert space fragmentation, which is caused by conserved quantities preventing thermalization.

Contribution

First experimental confirmation of Hilbert space fragmentation in a clean Bose-Hubbard system through direct observation of conserved quantities and slow dynamics.

Findings

Slow relaxation observed in strongly interacting regime

Conservation of singlons and doublons during dynamics

Experimental evidence supporting Hilbert space fragmentation

Abstract

While isolated quantum systems generally thermalize after long-time evolution, there are several exceptions defying thermalization. A notable mechanism of such nonergodicity is the Hilbert space fragmentation (HSF), where the Hamiltonian matrix splits into an exponentially large number of sectors due to the presence of nontrivial conserved quantities. Using ultracold gases, here we experimentally investigate the one-dimensional Bose-Hubbard system with neither disorder nor tilt potential, which has been predicted to exhibit HSF caused by a strong interatomic interaction. Specifically, we analyze far-from-equilibrium dynamics starting from a charge-density wave of doublons (atoms in doubly occupied sites) in a singlon and doublon-resolved manner to reveal a slowing-down of the relaxation in a strongly interacting regime. We find that the numbers of singlons and doublons are conserved during the dynamics, indicating HSF as a mechanism of the observed slow relaxation. Our results provide an experimental confirmation of the conserved quantities responsible for HSF.