  The standard mean-field theory for the Mott insulator-superfluid phase
transition is not sufficient to describe the Mott insulator-paired superfluid
phase transition. Therefore, by restricting the two-species Bose-Hubbard
Hamiltonian to the subspace of paired particles, and using perturbation theory,
here we derive an analytic mean-field expression for the Mott insulator-paired
superfluid transition boundary.
