Entanglement spectrum of the two dimensional Bose-Hubbard model

TL;DR

This paper analyzes the entanglement spectrum of the 2D Bose-Hubbard model, revealing boundary-dominated structures in the Mott phase and symmetry-breaking features in the superfluid phase, with implications for computational methods.

Contribution

It provides a detailed characterization of the entanglement spectrum across phases, highlighting boundary effects and symmetry-breaking signatures not previously fully understood.

Findings

Boundary-dominated entanglement spectrum in Mott phase

Distinct entanglement structures in superfluid phase

Evolution of entanglement features across the phase transition

Abstract

We study the entanglement spectrum (ES) of the Bose-Hubbard model on the two dimensional square lattice at unit filling, both in the Mott insulating and in the superfluid phase. In the Mott phase, we demonstrate that the ES is dominated by the physics at the boundary between the two subsystems. On top of the boundary-local (perturbative) structure, the ES exhibits substructures arising from one-dimensional dispersions along the boundary. In the superfluid phase, the structure of the ES is qualitatively different, and reflects the spontaneously broken U(1) symmetry of the phase. We attribute the basic low-lying structure to a so-called "tower of states" (TOS) Hamiltonian of the model. We then discuss how these characteristic structures evolve across the superfluid to Mott insulator transition and their influence on the behavior of the entanglement entropies. Finally, we briefly outline the implications of the ES structure on the efficiency of matrix-product-state based algorithms in two dimensions.