Spin-one bosons in low dimensional Mott insulating states

We analyze the strong coupling limit of spin-one bosons in low dimensional Mott insulating states. In 1D lattices, for an odd number of bosons per site ($N_0$), the ground state is a dimerized valence bond crystal state with a two-fold degeneracy; the low lying elementary spin excitations carry spin one. For an even number of bosons per site, the ground state is a nondegenerate spin singlet Mott state. We also argue that in a square lattice in a quantum disordered limit the ground states should be dimerized valence bond crystals for an odd integer $N_0$. Finally, we briefly report results for non-integer numbers of bosons per site in one-dimensional lattices.