Scale-invariance of parity-invariant three-dimensional QED

TL;DR

This paper provides numerical evidence that three-dimensional parity-invariant QED with two massless fermion flavors exhibits scale-invariance, characterized by the absence of a mass gap and specific anomalous dimensions, indicating critical behavior.

Contribution

It demonstrates scale-invariance in 3D parity-invariant QED using overlap fermions and finite-size scaling, revealing no bilinear condensate and estimating the mass anomalous dimension.

Findings

No bilinear condensate detected.

Scalar correlator's anomalous dimension matches the mass anomalous dimension.

Vector correlator remains non-anomalous.

Abstract

We present numerical evidences using overlap fermions for a scale-invariant behavior of parity-invariant three-dimensional QED with two flavors of massless two-component fermions. Using finite-size scaling of the low-lying eigenvalues of the massless anti-Hermitian overlap Dirac operator, we rule out the presence of bilinear condensate and estimate the mass anomalous dimension. The eigenvectors associated with these low-lying eigenvalues suggest critical behavior in the sense of a metal-insulator transition. We show that there is no mass gap in the scalar and vector correlators in the infinite volume theory. The vector correlator does not acquire an anomalous dimension. The anomalous dimension associated with the long-distance behavior of the scalar correlator is consistent with the mass anomalous dimension.