Phase diagram of lattice bosons in the presence of cavity-mediated and dipolar interactions

Long-range interactions in optical lattices have been extensively studied for more than one decade. Two types of long-range interactions, dipolar interactions and cavity-mediated long-range interactions, have been realized in experiments, and the phase diagrams for both systems have been obtained. However, when two types long-range interactions are competing with each other, the phase diagram of the system is still obscure. By means of large-scale Monte Carlo simulations, we study the competition between cavity-mediated and dipolar interactions in a system of lattice bosons. We also briefly present how to experimentally realize the phases stabilized by the extended Bose-Hubbard model describing the system.