Spectral functions of the honeycomb lattice with both the Hubbard and long-range Coulomb Interactions

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.