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Bond order via cavity-mediated interactions

We numerically study the phase diagram of bosons tightly trapped in the lowest band of an optical lattice and dispersively coupled to a single-mode cavity field. The dynamics is encompassed by an extended Bose-Hubbard model. Here, the cavity-mediated interactions are described by a two-body potential term with a global range and by a correlated tunneling term where the hopping amplitude depends on a global observable. We determine the ground state properties in one dimension by means of the density matrix renormalization group algorithm, focusing on the effects due to the correlated tunneling. The latter is responsible for the onset of bond orders, manifesting in one insulating and two gapless bond ordered phases. We discuss the resulting phases for different geometries that correspond to different relative strengths of the correlated tunneling coefficient. We finally analyze the scaling of the entanglement entropy in the gapless bond ordered phases that appear entirely due to global interactions and determine the corresponding central charges.