  In this paper we investigate possible spin disordered phase in the Hubbard
model on the honeycomb lattice. Using a slave-particle theory that include the
charge fluctuations, we find a meanfield spin disordered phase in a range of
on-site repulsion $U$. The spin disordered state is described by gapped
fermions coupled to compact U(1) gauge field. We study the
confinement/deconfinement problem of the U(1) gauge theory due to the
instantons proliferation. We calculate all allowed instanton terms and compute
their quantum numbers. It is shown that the meanfield spin disordered phase is
unstable. The instantons proliferation induce a translation symmetry breaking.
