Weak Fragmentation and Thermalization in a Dipole-Conserving Bose-Hubbard Chain

TL;DR

This paper investigates how weak Hilbert-space fragmentation affects thermalization and chaos in a dipole-conserving Bose-Hubbard chain, revealing a transition from thermal to nonergodic behavior with increasing interactions.

Contribution

It demonstrates that weak fragmentation does not prevent quantum chaos or thermalization and introduces a minimal model for studying ergodicity breaking in dipole-conserving systems.

Findings

Weak Hilbert-space fragmentation observed in the model.

Constructed exponentially large family of frozen states.

Identified transition from thermal to nonergodic regime with increasing interaction.

Abstract

We study Hilbert-space fragmentation and thermalization in a one-dimensional dipole-conserving Bose-Hubbard chain. By analyzing the structure of the Hamiltonian matrix in the Fock basis, we show that the system exhibits weak Hilbert-space fragmentation. We further construct an exponentially large family of frozen product states and derive analytical upper and lower bounds on their number. Using exact diagonalization, we examine the consequences of weak fragmentation for eigenstate half-chain entanglement, density relaxation dynamics, and level statistics. All these quantities reveal a transition from a weak eigenstate thermalization regime to a nonergodic regime with increasing on-site interaction strength. These results show that weak Hilbert-space fragmentation \textit{does not} preclude quantum chaos or thermalization, and provides a minimal platform for studying the interplay of dipole conservation, weak fragmentation, and ergodicity breaking.