Renormalization of Coulomb interaction in graphene: computing observable quantities

TL;DR

This paper develops a perturbative renormalization scheme for Coulomb interactions in graphene, focusing on the Fermi velocity and optical conductivity, providing a systematic way to handle divergences in physical observable calculations.

Contribution

It introduces a method to renormalize divergences in graphene's Coulomb interaction calculations by focusing on the Fermi velocity, applicable to observable quantities like optical conductivity.

Findings

Divergences are linked to the electron self-energy and can be renormalized via Fermi velocity adjustments.

Second-order perturbation theory renormalization of photon polarization is achieved.

The approach clarifies how to compute physical observables in interacting graphene systems.

Abstract

We address the computation of physical observables in graphene in the presence of Coulomb interactions of density-density type modeled with a static Coulomb potential within a quantum field theory perturbative renormalization scheme. We show that all the divergences encountered in the physical quantities are associated to the one loop electron self-energy and can be determined without ambiguities by a proper renormalization of the Fermi velocity. The renormalization of the photon polarization to second order in perturbation theory - a quantity directly related to the optical conductivity - is given as an example.