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

Gauge theory of the Hubbard model on honeycomb lattice and its instanton effect