Monte Carlo Simulation of the Semimetal-Insulator Phase Transition in Monolayer Graphene

TL;DR

This paper models the low-energy electronic behavior of monolayer graphene using a 2+1D fermion field theory, exploring the semimetal-insulator transition via Monte Carlo simulations and analyzing critical phenomena.

Contribution

It provides the first numerical analysis of the quasiparticle propagator and critical exponents at the transition in a contact-interaction fermion model for graphene.

Findings

Identified the critical coupling for the phase transition.

Measured critical exponents, including the dynamical critical exponent.

Analyzed the universality and implications for physical 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=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 insulting phase. We present results of an extensive numerical study of the model's critical region, including the order parameter, its associated susceptibility, and for the first time the quasiparticle propagator. The data enables an extraction of the critical exponents at the transition, including the dynamical critical exponent, which are hypothesised 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.