Entanglement entropy across the superfluid-insulator transition : a signature of bosonic criticality

TL;DR

This paper investigates how entanglement entropy behaves across the superfluid-insulator transition in the Bose-Hubbard model, revealing a sharp singularity and unique signatures of different bosonic criticalities.

Contribution

It provides a detailed analysis of entanglement properties across the transition using a slave-boson approach, highlighting signatures of bosonic criticality and the role of the Higgs mode.

Findings

Entanglement entropy shows a sharp singularity at the transition.

Enhanced singularity at fixed, integer filling due to a gapless Higgs mode.

Distinct entanglement signatures differentiate types 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.