Anomalous pairing of bosons: Effect of multi body interactions in optical lattice

An interesting first order type phase transition between Mott lobes has been reported in Phys. Rev. Lett. 109, 135302 (2012) for a two-dimensional Bose-Hubbard model in the presence of attractive three-body interaction. We re-visit the scenario in a system of ultracold bosons in a one-dimensional optical lattice using the density matrix renormalization group method and show that an unconventional pairing of particles occurs due to the competing two-body repulsive and three-body attractive interactions. This leads to a pair superfluid phase sandwiched between the Mott insulator lobes corresponding to densities $\rho=1$ and $\rho=3$ in the strongly interacting regime. We further extend our analysis to a two dimensional Bose-Hubbard model using the self consistent cluster-mean-field theory approach and confirm that the unconventional pair superfluid phase stabilizes in the region between the Mott lobes in contrast to the direct first order jump as predicted before. In the end we establish connection to the most general Bose-Hubbard model and analyse the fate of the pair superfluid phase in presence of an external trapping potential.