Phase Transitions in a Bose-Hubbard Model with Cavity-Mediated Global-Range Interactions

TL;DR

This paper investigates phase transitions in a Bose-Hubbard model with competing local and global interactions, revealing multiple phases and excitation modes through mean-field and Monte Carlo analyses.

Contribution

It introduces a comprehensive phase diagram for the model, identifying four distinct phases and characterizing their transitions and excitation spectra.

Findings

Identifies four phases: superfluid, supersolid, Mott insulator, charge density wave.

Characterizes phase transitions as first or second order.

Discovers softening of excitations leading to Higgs and roton modes.

Abstract

We study a system with competing short- and global-range interactions in the framework of the Bose-Hubbard model. Using a mean-field approximation we obtain the phase diagram of the system and observe four different phases: a superfluid, a supersolid, a Mott insulator and a charge density wave, where the transitions between the various phases can be either of first or second order. We qualitatively support these results using Monte-Carlo simulations. An analysis of the low-energy excitations shows that the second-order phase transition from the charge density wave to the supersolid is associated with the softening of particle- and hole-like excitations which give rise to a gapless mode and an amplitude Higgs mode in the supersolid phase. This amplitude Higgs mode is further transformed into a roton mode which softens at the supersolid to superfluid phase transition.