  We have developed a Hartree-Fock theory for electrons on a honeycomb lattice
aiming to solve a long-standing problem of the Fermi velocity renormalization
in graphene. Our model employs no fitting parameters (like an unknown band
cutoff) but relies on a topological invariant (crystal structure function) that
makes the Hartree-Fock sublattice spinor independent of the electron-electron
interaction. Agreement with the experimental data is obtained assuming static
self-screening including local field effects. As an application of the model,
we derive an explicit expression for the optical conductivity and discuss the
renormalization of the Drude weight. The optical conductivity is also obtained
via precise quantum Monte Carlo calculations which compares well to our
mean-field approach.
