  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.
