Lattice field theory simulations of graphene

Understand

We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene.

• We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles.
• The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis.
• A thorough discussion of finite-size effects is given, along with several tests of our calculational framework.