Renormalization group approach to 2D Coulomb interacting Dirac fermions with random gauge potential

TL;DR

This paper studies how 2D massless Dirac fermions with Coulomb interactions and random gauge fields behave at different scales, revealing a complex fixed point structure and critical behavior using perturbative methods.

Contribution

It demonstrates the existence of a manifold of fixed points for 2D Dirac fermions with Coulomb and disorder interactions, extending previous results and analyzing their stability and critical properties.

Findings

Identification of a stable fixed curve at weak interactions and disorder

Merging of fixed points at a critical endpoint with z=1

Confirmation of previous results with extended analysis

Abstract

We argue that massless Dirac particles in two spatial dimensions with $1/r$ Coulomb repulsion and quenched random gauge field are described by a manifold of fixed points which can be accessed perturbatively in disorder and interaction strength, thereby confirming and extending the results of arXiv:0707.4171. At small interaction and small randomness, there is an infra-red stable fixed curve which merges with the strongly interacting infra-red unstable line at a critical endpoint, along which the dynamical critical exponent $z=1$.