Revisiting pairing of bosons in one-dimensional Bose–Hubbard model with three-body interaction using CMFT+DMRG method

We revisit the Bose–Hubbard model with hard-core three-body attractive interactions in one-dimension using the cluster mean-field theory with the density-matrix renormalization group. Our study focuses on the region of the phase diagram between density one Mott MI(1) and density three Mott MI(3) insulator lobes and studies the pairing of bosons. We calculate the order parameters and condensate factors corresponding to atomic and pair superfluid phases. We find no phase transition directly from MI(1) to MI(3) when the attractive three-body interaction is present. The pair superfluid dominates the region between MI(1) and MI(3) when the hopping parameter is small. As the hopping parameter increases, the model shows a phase transition to the atomic superfluid. However, the paring of bosons persists even in the atomic superfluid phases. We finally obtain the phase diagram and compare it with earlier results.