Double-well Bose-Hubbard model with nearest-neighbor and cavity-mediated long-range interactions

We consider a one-dimensional Bose -Hubbard model (BHM) with on -site double -well potentials and study the effect of nearest -neighbor repulsion and cavity -mediated long-range interactions by calculating the ground -state phase diagrams with quantum Monte Carlo simulations. We show that when the intrawell repulsion is as strong as the on -site repulsion, a dimerized Mott -insulator phase appears at the tip of the dimerized density -wave phase for a density of one particle per double well. Furthermore, we find a dimerized Haldane -insulator phase in the double -well BHM with nearest -neighbor interaction, which is identical to a dimerized BHM with repulsive interactions up to the third neighbor.