Quantum Phase Transition in a Graphene Model

TL;DR

This paper investigates the quantum phase transition in a graphene-like model using Monte Carlo simulations, focusing on the critical behavior and exponents near the transition point.

Contribution

It provides the first non-perturbative numerical analysis of the critical properties of a graphene model with Coulomb interactions.

Findings

Quantum phase transition occurs at N_f ~ 4.7 fermion species.

Critical exponents are calculated at the transition.

The model exhibits a transition from a semimetal to an insulating phase.

Abstract

We present results for the equation of state of a graphene-like model in an effort to understand the properties of its quantum phase transition. The N_f fermion species interact through a three dimensional instantaneous Coulomb potential. Since there are no reliable analytical tools that work for all values of N_f and the coupling constant g, we rely on Monte Carlo simulations to calculate the critical properties of the model near the phase transition. We consider the four-component formulation for the fermion fields, which arises naturally as the continuum limit of the staggered fermion construction in (2+1) dimensions. In the limit of infinitely strong Coulomb interaction, the system undergoes a quantum phase transition at a critical number of fermion species N_fc ~ 4.7. We also calculate the values of the critical exponents at the quantum phase transition.