Green functions in graphene monolayer with Coulomb interactions taken into account

We consider the low energy effective field model of graphene monolayer. Coulomb interactions are taken into account. The model is simulated numerically using the lattice discretization with staggered fermions. The two point fermionic Green functions are calculated. We find that in the insulator phase these Green functions almost do not depend on energy. This indicates that the effective field model (in its insulator phase) does not correspond to the real graphene.

► We consider the low energy effective field model of graphene.
► The model is simulated numerically using lattice discretization.
► Two point Green functions are calculated.
► This effective model is not self-consistent at small beta.