  We have investigated spin singlet Mott states of spin-one bosons with
antiferromagnetic interactions. These spin singlet states do not break
rotational symmetry and exhibit remarkably different macroscopic properties
compared with nematic Mott states of spin-one bosons. We demonstrate that the
dynamics of spin singlet Mott states is fully characterized by even- and
odd-class quantum dimer models. The difference between spin singlet Mott states
for even and odd numbers of atoms per site can be attributed to a selection
rule in the low energy sectors of on-site Hilbert spaces; alternatively, it can
also be attributed to an effect of Berry's phases on bosonic Mott states.
  We also discuss evidence for spin singlet quantum condensate of spin-one
atoms. Our main finding is that in a projected spin singlet Hilbert space, the
low energy physics of spin-one bosons is fully characterized by a Bose-Hubbard
model of interacting spinless bosons carrying charges of Ising gauge fields;
the other major finding is spin-charge separation in some one-dimensional Mott
states. We propose charge-e spin singlet superfluid for an odd number of atoms
per lattice site and charge-2e spin singlet superfluid for an even number of
atoms per lattice site in one-dimensional lattices. All discussions in this
article are limited to integer numbers of bosons per site.
