Extended Bose-Hubbard Model with Cavity-Mediated Infinite-Range Interactions at Finite Temperatures.

We consider the finite-temperature properties of the extended Bose-Hubbard model realized recently in an ETH experiment [Nature 532, 476 (2016)]. Competing short- and global-range interactions accommodate fascinating collective phenomena. We formulate a self-consistent mean-field theory to describe the behaviors of the system at finite temperatures.