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Quantum phases of attractive bosons on a Bose-Hubbard ladder with three-body constraint

We obtain the complete quantum phase diagram of bosons on a two-leg ladder in the presence of attractive onsite and repulsive interchain nearest-neighbor interactions by imposing the onsite three-body constraint. We find three distinct phases; namely, the atomic superfluid (ASF), dimer superfluid (DSF), and the dimer rung insulator (DRI). In the absence of the interchain nearest-neighbor repulsion, the system exhibits a transition from the ASF to the DSF phase with increasing onsite attraction. However, the presence of the interchain nearest-neighbor repulsion stabilizes a gapped DRI phase, which is flanked by the DSF phase. We also obtain the phase diagram of the system for different values of the interchain nearest-neighbor interaction. By evaluating different order parameters, we obtain the complete phase diagram and the properties of the phase transitions using the self-consistent cluster mean-field theory.