Rigorous construction of ground state correlations in graphene: renormalization of the velocities and Ward Identities

We consider the two-dimensional Hubbard model on the honeycomb lattice, as a model for single-layer graphene with screened Coulomb interactions; at half filling and weak coupling, we construct its ground-state correlations by a convergent multiscale expansion, rigorously excluding the presence of magnetic or superconducting instabilities or the formation of a mass gap. The Fermi velocity, which can be written in terms of a convergent series expansion, remains close to its noninteracting value and turns out to be isotropic; as a consequence, the Dirac cones are isotropic at low energies. On the contrary, the interaction produces an asymmetry between the two components of the charge velocity, in contrast to the predictions based on relativistic or continuum approximations.