Eigenstate entanglement entropy in Bose-Hubbard models

TL;DR

This paper investigates the entanglement entropy of mid-spectrum eigenstates in Bose-Hubbard models, deriving volume-law coefficients and analyzing subleading contributions, revealing effects of disorder and particle-number conservation.

Contribution

It generalizes mean-field approaches to bosonic systems with tunable local cutoffs and explores how disorder and conservation laws affect entanglement entropy.

Findings

Volume-law coefficient matches previous analytical and numerical results.

Breaking translational invariance does not alter the volume-law contribution.

Subleading O(1) term depends on particle density and cutoff, with potential universality without particle conservation.

Abstract

While the eigenstate entanglement entropy has been extensively studied for fermionic systems, much less is known about bosonic systems. Here, we study the entanglement entropy of mid-spectrum eigenstates of Bose-Hubbard models, focusing on weakly disordered models with and without particle-number conservation, and contrasting them with the translationally-invariant model. We analyze the volume-law and O(1) contributions to the entanglement entropy via the averages over mid-spectrum eigenstates and the corresponding distributions. We derive the volume-law coefficient of the entanglement entropy by generalizing the mean-field approach from [Phys. Rev. Lett. 119, 220603 (2017)] to many-body systems with a tunable local bosonic cutoff, which agrees with previous analytical and numerical results from [Phys. Rev. B 110, 235154 (2024)]. We show that the volume-law contribution to the entanglement entropy does not change upon breaking translational invariance via on-site disorder. We then numerically study the role of the subleading O(1) contribution to the entanglement entropy. We find that, in the particle-number conserving case, it exhibits a nontrivial dependence on the particle-number density and the local bosonic cutoff, while without particle-number conservation, results suggest the emergence of a universal O(1) contribution beyond the random pure state predictions.