Quantum Critical Behaviour in a Graphene-like Model

TL;DR

This paper uses numerical simulations to study a graphene-like fermion model in 2+1 dimensions, identifying a quantum critical point and analyzing phase transitions relevant to real graphene.

Contribution

First numerical analysis of a 2+1D fermion model for graphene, identifying a critical flavor number and characterizing quantum phase transitions.

Findings

Critical flavor number N_fc=4.8(2) separates insulating and conducting phases.

Estimated critical exponents at the quantum critical point.

Evidence of strong correlations in the weak-coupling regime for N_f=2.

Abstract

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. Strong correlations are evident in the weak-coupling regime.