Random matrix model for QCD_3 staggered fermions

TL;DR

This paper demonstrates that the eigenvalue density of staggered fermions in lattice QCD_3 resembles that of QCD_4 and introduces a two-matrix model to describe its evolution with lattice coupling.

Contribution

It reveals the unexpected similarity in eigenvalue densities between QCD_3 and QCD_4 and proposes a two-matrix model to interpolate their behaviors as lattice coupling varies.

Findings

Eigenvalue density in QCD_3 matches QCD_4 at small lattice coupling.

Eigenvalue density evolves towards non-chiral matrix model predictions with increasing beta.

A two-matrix model effectively captures the evolution pattern of eigenvalue density.

Abstract

We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice QCD_3 at small lattice coupling constant beta has exactly the same shape as in QCD_4. This observation is quite surprising, since universal properties of the QCD_3 Dirac operator are expected to be described by a non-chiral matrix model. We show that this effect is related to the specific nature of the staggered fermion discretization and that the eigenvalue density evolves towards the non-chiral random matrix prediction when beta is increased and the continuum limit is approached. We propose a two-matrix model with one free parameter which interpolates between the two limits and very well mimics the pattern of evolution with beta of the eigenvalue density of the staggered fermion operator in QCD_3.