Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids

TL;DR

This paper performs a two-loop field theoretic renormalization of reduced quantum electrodynamics, revealing insights into Dirac liquids like graphene and their ultra-relativistic limits, including optical conductivity and fermion anomalous dimensions.

Contribution

It provides a detailed two-loop renormalization analysis of reduced QED, clarifying its structure and applications to Dirac liquids and ultra-relativistic graphene.

Findings

Recovered interaction correction to optical conductivity: C*=(92-9π^2)/(18π)

Derived anomalous dimension of fermion field: γ_ψ(ᾱ,ξ)

Clarified the structure of reduced QED using BPHZ prescription

Abstract

The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphene-like materials, the surface states of some topological insulators and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use of the BPHZ prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultra-relativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity: $\mathcal{C}^*=(92-9\pi^2)/(18\pi)$ and the anomalous dimension of the fermion field: $\gamma_{\psi}(\bar{\alpha},\xi) = 2 \bar{\alpha}\,(1-3\xi)/3 -16\,\left( \zeta_2 N_F + 4/27 \right)\, \bar{\alpha}^2 + O(\bar{\alpha}^3)$, where $\bar{\alpha} = e^2/(4\pi)^2$ and $\xi$ is the gauge-fixing parameter.