  We study spontaneous symmetry breaking in a system of spinless fermions in
the Honeycomb lattice paying special emphasis to the role of an enlarged unit
cell on time reversal symmetry broken phases. We use a tight binding model with
nearest neighbor hopping t and Hubbard interaction V1 and V2 and extract the
phase diagram as a function of electron density and interaction within a mean
field variational approach. The analysis completes the previous work done in
Phys. Rev. Lett. 107, 106402 (2011) where phases with non--trivial topological
properties were found with only a nearest neighbor interaction V1 in the
absence of charge decouplings. We see that the topological phases are
suppressed by the presence of metallic charge density fluctuations. The
addition of next to nearest neighbor interaction V2 restores the topological
non-trivial phases.
