Anomalous behavior in an effective model of graphene with Coulomb interactions

TL;DR

This paper uses exact Renormalization Group methods to study the infrared behavior of an effective graphene model with Coulomb interactions, revealing fixed points and critical exponents affecting quasiparticle properties.

Contribution

It provides a rigorous RG analysis of an effective graphene model, showing how interactions influence low-energy properties and fixed points.

Findings

Effective charges tend to a line of fixed points.

Quasiparticle weight vanishes at small momenta.

Fermi velocity approaches a finite value with power law behavior.

Abstract

We analyze by exact Renormalization Group (RG) methods the infrared properties of an effective model of graphene, in which two-dimensional massless Dirac fermions propagating with a velocity smaller than the speed of light interact with a three-dimensional quantum electromagnetic field. The fermionic correlation functions are written as series in the running coupling constants, with finite coefficients that admit explicit bounds at all orders. The implementation of Ward Identities in the RG scheme implies that the effective charges tend to a line of fixed points. At small momenta, the quasi-particle weight tends to zero and the effective Fermi velocity tends to a finite value. These limits are approached with a power law behavior characterized by non-universal critical exponents.