The Index Theorem and Random Matrix Theory for Improved Staggered Quarks

TL;DR

This paper demonstrates that improved staggered quarks in lattice QCD accurately reflect QCD topology and spectral properties, aligning with the Index Theorem and random matrix theory predictions near the continuum limit.

Contribution

It provides evidence that improved staggered quark operators correctly reproduce topological and spectral features predicted by QCD and random matrix theory.

Findings

Eigenvalue spectrum separates into zero modes and others as expected.

Non-zero modes cluster into quartets approaching the continuum limit.

Random matrix theory predictions are well matched in the epsilon regime.

Abstract

We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD. We find a clear separation of the spectrum of eigenvalues into high chirality, would-be zero modes and others, in accordance with the Index Theorem. We find the expected clustering of the non-zero modes into quartets as we approach the continuum limit. The predictions of random matrix theory for the epsilon regime are well reproduced. We conclude that improved staggered quarks near the continuum limit respond correctly to QCD topology.