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

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.

19 pages, 4+9 figures

References in corpus (10)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Dynamical properties of ultracold bosons in an optical lattice
• Bose-glass phases of ultracold atoms due to cavity backaction
• Entanglement entropy scaling in the bilayer Heisenberg spin system
• Thermodynamic singularities in the entanglement entropy at a 2D quantum critical point
• Many-body localization in presence of cavity mediated long-range interactions
• Fully quantum scalable description of driven dissipative lattice models
• Mean-field phase diagram of ultracold atomic gases in cavity quantum electrodynamics
• Models with short and long-range interactions: phase diagram and reentrant phase
• Residual entropy and critical behavior of two interacting boson species in a double well

Cited by in corpus (3)

• Enhancement of chiral edge currents in ($d$+1)-dimensional atomic Mott-band hybrid insulators
• Logarithmic, Fractal and Volume-Law Entanglement in a Kitaev chain with long-range hopping and pairing
• Tunable boson-assisted finite-range interaction and engineering Majorana corner modes in optical lattices