Spectral functions of lattice fermions on the honeycomb lattice with Hubbard and long-range Coulomb interactions

The absence of screening of the nonlocal 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 near the phase transition, are primarily determined by the local effective Hubbard interaction. In the weakly interacting regime, the long-range Coulomb interaction enhances the bandwidth of quasiparticles and suppresses their lifetime. Conversely, near the phase transition, the long-range Coulomb interaction suppresses the background antiferromagnetic fluctuation, which potentially promotes the propagation of spin polarons, leading to a slight enhancement of the quasiparticle spectral weight and lifetime.