Paired state in an integrable spin-1 boson model

An exactly solvable model describing the low-density limit of the spin-1 bosons in a one-dimensional optical lattice is proposed. The exact Bethe ansatz solution shows that the low-energy physics of this system is described by a quantum liquid of spin singlet bound pairs. Motivated by the exact results, a mean-field approach to the corresponding three-dimensional system is carried out. Condensation of singlet pairs and coexistence with ordinary Bose-Einstein condensation are predicted.