Monte Carlo simulation of the semimetal-insulator phase transition in monolayer graphene

Abstract

A $2+1$-dimensional fermion field theory is proposed as a model for the low-energy electronic excitations in monolayer graphene. The model consists of ${N}_{f}=2$ four-component Dirac fermions moving in the plane and interacting via a contact interaction between charge densities. For strong couplings there is a continuous transition to a Mott insulating phase. We present results of an extensive numerical study of the model's critical region, including the order parameter, its associated susceptibility, and the quasiparticle propagator. The data enable an extraction of the critical exponents at the transition (including the dynamical critical exponent) which are hypothesized to be universal features of a quantum critical point. The relation of our model with others in the literature is discussed along with the implications for physical graphene following from our value of the critical coupling.