Ground State Properties of Graphene In Hartree-Fock Theory

We study the Hartree-Fock approximation of graphene in in - nite volume, with instantaneous Coulomb interactions. First we construct its translation-invariant ground state and we recover the well-known fact that, due to the exchange term, the e ective Fermi velocity is logarithmically divergent at zero momentum. In a second step we prove the existence of a ground state in the presence of local defects and we discuss some properties of the linear response to an external electric eld. All our results are non perturbative.