How electrons Coulomb repulsion changes graphene band structure

Base on effective medium theory we introduce a multi sites method for calculation of realistic energy bands of strongly correlated systems. We found due to approximated self energy, the density of states that obtained directly by calculated local Green function does not reflects system energy bands truly. By using this method we investigated how electrons repulsion renormalizes graphene bands. Graphene realistic bands calculated in both the dynamical mean field theory (DMFT) and four sites beyond super cell approximation for different repulsions. Our calculated interacting graphene bands illustrate a semi metal to a Mott insulator anti ferromagnetic phase transition at repulsions [Formula: see text] and [Formula: see text] for DMFT and four sites beyond super cell approximation respectively. These values are much less than finite size quantum Monte Carlo calculation prediction. We showed that the graphene bands are very sensitive to electrons repulsions and this phase transition happens at low repulsions in comparison to graphene band width.