Is suspended graphene an insulator?

Graphene at low energies resembles massless quantum electrodynamics in a strongly coupled regime, away from the usual perturbative region where the fine structure constant is $\alpha \simeq 1/137$. Indeed, a single sheet of graphite in vacuum presents $\alpha \sim 1$. At such strong couplings the U(4) chiral symmetry of graphene can spontaneously break, inducing a gap in the quasiparticle spectrum. The question of whether chiral symmetry is broken represents a computational challenge that lies outside the domain of analytic techniques. In this talk, we will present the results of the first Monte Carlo simulation of the low-energy effective theory of graphene in vacuum (see abstract by T.~A.~L\"ahde). We have computed the chiral condensate, which is the order parameter for the insulating charge density wave state, as a function of $\alpha$, and found a chiral phase transition that is compatible with suspended graphene being in the gapped phase.