Many-body effects on graphene conductivity: Quantum Monte Carlo calculations

Optical conductivity of graphene is studied using Quantum Monte Carlo calculations. We start from Euclidean current-current correlator and extract $\sigma (\omega)$ from Green-Kubo relations using Backus-Gilbert method. Calculations were performed both for long-range interactions and taking into account only contact term. In both cases we vary interaction strength and study its influence on optical conductivity. We compare our results with previous theoretical calculations choosing $\omega \approx \kappa$ thus working in the region of the plateau in $\sigma(\omega)$ which corresponds to optical conductivity of Dirac quasiparticles. No dependence of optical conductivity on interaction strength is observed unless we approach antiferromagnetic phase transition in case of artificially enhanced contact term. Our results strongly support previous theoretical studies claimed very weak regularization of graphene conductivity.