  The absence of screening of the non-local Coulomb interaction in Dirac
systems at charge neutrality leads to the breakdown of the Fermi liquid and
divergence of the Fermi velocity. On the other hand, Mott Hubbard physics and
the concomitant formation of local moments is dominated by the local effective
Hubbard interaction. Using quantum Monte Carlo methods combined with stochastic
analytical continuation, we compute the single particle spectral function of
fermions on the honeycomb lattice for a realistic interaction that includes
both the Hubbard interaction and long-ranged Coulomb repulsion. To a first
approximation, we find that the generic high-energy features such as the
formation of the upper Hubbard band are independent of the long-ranged Coulomb
repulsion and determined mostly by the local effective Hubbard interaction. The
sub-leading effects of adding the long-range interaction include an enhancement
of the bandwidth and a decrease of the spin-polaron quasi-particle weight and
lifetime.
