We study the entanglement entropy and entanglement spectrum of the paradigmatic Bose-Hubbard model, describing strongly correlated bosons on a lattice. The use of a controlled approximation—the slave-boson approach—allows us to study entanglement in all regimes of the model (and, most importantly, across its superfluid–Mott-insulator transition) at a minimal cost. We find that the area-law scaling of entanglement—verified in all the phases—exhibits a sharp singularity at the transition. The singularity is greatly enhanced when the transition is crossed at fixed, integer filling, due to a richer entanglement spectrum containing an additional gapless mode, which descends from the amplitude (Higgs) mode of the global excitation spectrum—while this mode remains gapped at the generic (commensurate-incommensurate) transition with variable filling. Hence, the entanglement properties contain a unique signature of the two different forms of bosonic criticality exhibited by the Bose-Hubbard model.

• Received 10 December 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.190401