Entanglement spectrum of the two dimensional Bose-Hubbard model

Understand

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.