We introduce effective field theories for the electronic properties of graphene in terms of relativistic fermions propagating in 2+1 dimensions, and outline how strong inter-electron interactions may be modelled by numerical simulation of a lattice field theory. For strong enough coupling an insulating state can form via condensation of particle-hole pairs, and it is demonstrated that this is a theoretical possibility for monolayer graphene. For bilayer graphene the effect of an interlayer bias voltage can be modelled by the introduction of a chemical potential (akin to isopsin chemical potential in QCD) with no accompanying sign problem; simulations reveal the presence of strong interactions among the residual degrees of freedom at the resulting Fermi surface, which is disrupted by an excitonic condensate. We also present preliminary results for the quasiparticle dispersion, which permit direct estimates of both the Fermi momentum and the induced gap.

invited talk at 9th International Workshop on Critical Point and Onset of Deconfinement - CPOD2014, 17-12 November 2014, ZiF, University of Bielefeld, Germany