Spinor Bosonic Atoms in Optical Lattices: Symmetry Breaking and Fractionalization

We study superfluid and Mott insulator phases of cold spin-1 Bose atoms with antiferromagnetic in- teractions in an optical lattice, including a usual polar condensate phase, a condensate of singlet pairs, a crystal spin nematic phase, and a spin singlet crystal phase. We suggest a possibility of exotic fraction- alized phases of spinor Bose-Einstein condensates and discuss them in the language of Z2 lattice gauge theory.Physic