No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions

TL;DR

This study numerically investigates three-dimensional QED with multiple fermion flavors, providing evidence against the existence of a bilinear condensate and suggesting critical behavior in the system.

Contribution

It offers the first comprehensive lattice analysis of parity-invariant 3D QED with various fermion flavors, challenging previous assumptions about condensate formation.

Findings

Eigenvalues do not scale with inverse volume.

Eigenvector IPR shows multi-fractal scaling.

Number variance indicates critical behavior.

Abstract

We present our numerical study of three-dimensional QED with 2, 4, 6 and 8 flavors of massless two-component fermions using a parity-preserving lattice regularization with Wilson fermions. We study the behavior of low-lying eigenvalues of the massless improved Wilson-Dirac operator as a function of three-dimensional physical volume, after taking the continuum limit at fixed physical volumes. We find the following evidences against the presence of bilinear condensate: the eigenvalues do not scale as the inverse of the three-dimensional physical volume, and the number variance associated with these eigenvalues do not exhibit ergodic behavior. The inverse participation ratio (IPR) of the associated eigenvectors exhibits a multi-fractal volume scaling. The relation satisfied by number variance and IPR suggests critical behavior.