title: Entanglement Entropy across the Superfluid-Insulator Transition: A Signature of Bosonic Criticality.
abstract: 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.
authors.affiliation: Université de Lyon, Ens de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France.
authors.forename: Irénée
authors.initials: I
authors.lastname: Frérot
authors.affiliation: Université de Lyon, Ens de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France.|Institut Universitaire de France, 103 boulevard Saint-Michel, 75005 Paris, France.
authors.forename: Tommaso
authors.initials: T
authors.lastname: Roscilde