The exact vanishing of the interaction corrections to the zero temperature optical conductivity of undoped graphene in the presence of weak short-range interactions is rigorously established. Our results are in agreement with measurements of graphene’s ac conductivity in a range of frequencies between the temperature and the bandwidth. Even if irrelevant in the renormalization group sense, lattice effects and nonlinear bands are essential for the universality of the conductivity.

• Received 1 March 2011

DOI:https://doi.org/10.1103/PhysRevB.83.195401