Deconstructing entanglement in the 1D Bose-Hubbard model: bipartite fluctuations and symmetry-resolved entanglement

In quantum many-body systems of itinerant particles, the entanglement between spatial subregions comprises entanglement due to particle fluctuations between subregions, and the symmetry-resolved entanglement–the entanglement within each subsystem particle number sector. Here we present a numerical study of this entanglement structure in the Bose-Hubbard model in one spatial dimension, a paradigmatic and experimentally relevant itinerant boson system. Using a path integral quantum Monte Carlo method, we have performed a numerical analysis of the subsystem scaling and finite-size scaling of the Rényi entanglement entropy, bipartite number fluctuations, and symmetry resolved Rényi entanglement entropy in the 1D Bose-Hubbard ground state. We demonstrate the dependence of these scalings on the Luttinger parameter in the superfluid phase, as predicted by Luttinger liquid theory. Additionally, we explore the scaling of the operationally accessible entanglement near the critical point.