Quantum Critical Behaviour in a Graphene-like Model

Understand

We present the first results of numerical simulations of a 2+1 dimensional fermion field theory based on a recent proposal for a model of graphene, consisting of N_f four-component Dirac fermions moving in the plane and interacting via an instantaneous Coulomb interaction.

• In the strong-coupling limit we identify a critical number of flavors N_fc=4.8(2) separating an insulating from a conducting phase.
• This transition corresponds to the location of a quantum critical point, and we use a fit to the equation of state for the chiral order parameter to estimate the critical exponents.
• Next we simulate N_f=2 corresponding to real graphene, and approximately locate a transition from strong to weak coupling behaviour.