Ground state properties of graphene in Hartree-Fock theory
  We study the Hartree-Fock approximation of graphene in infinite 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 effective 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 field. All our results are non perturbative. 
Christian Hainzl, Mathieu Lewin, Christof Sparber
math-ph cond-mat.mes-hall cond-mat.other math.MP