Quantum critical behavior of entanglement in lattice bosons with cavity-mediated long-range interactions

TL;DR

This paper investigates the entanglement entropy behavior in an extended Bose-Hubbard model with cavity-mediated long-range interactions, revealing critical phenomena at phase transitions including a unique logarithmic term at the superfluid-to-supersolid transition.

Contribution

It introduces a slave-boson approach to analyze entanglement entropy in a model with competing interactions, uncovering novel critical behavior at phase transitions.

Findings

Singularity in entanglement entropy at insulator-superfluid transition.

Critical logarithmic term at superfluid-to-supersolid transition.

Emergence of a gapless roton mode at the critical point.

Abstract

We analyze the ground-state entanglement entropy of the extended Bose-Hubbard model with infinite-range interactions. This model describes the low-energy dynamics of ultracold bosons tightly bound to an optical lattice and dispersively coupled to a cavity mode. The competition between onsite repulsion and global cavity-induced interactions leads to a rich phase diagram, which exhibits superfluid, supersolid, and insulating (Mott and checkerboard) phases. We use a slave-boson treatment of harmonic quantum fluctuations around the mean-field solution and calculate the entanglement entropy across the phase transitions. At commensurate filling, the insulator-superfluid transition is signalled by a singularity in the area-law scaling coefficient of the entanglement entropy, that is similar to the one reported for the standard Bose-Hubbard model. Remarkably, at the continuous $\mathbb{Z}_2$ superfluid-to-supersolid transition we find a critical logarithmic term, regardless of the filling. This behavior originates from the appearance of a roton mode in the excitation and entanglement spectrum, becoming gapless at the critical point, and it is characteristic of collective models.