  We investigate various quantum phase transitions of attractive two-species
bosons in a square lattice. Using the algorithm based on the tensor product
states, the phase boundaries of the pair superfluid states with nonzero pair
condensate density \emph{and} vanishing atomic condensate density are
determined. Various quantum phase transitions across the phase boundaries are
characterized. Our work thus provides guides to the experimental search of the
pair superfluid phase in lattice boson systems.
