The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks

TL;DR

This paper investigates improved staggered quark Dirac operators in lattice QCD, demonstrating their spectral properties align with theoretical expectations and approach continuum behavior, especially regarding topology and eigenvalue clustering.

Contribution

It provides evidence that improved actions enhance the continuum-like spectral and topological properties of staggered quarks in lattice QCD.

Findings

Spectrum separates into zero modes and others as expected.

Number of zero modes matches topological charge predictions.

Eigenvalues cluster into quartets and match random matrix theory predictions.

Abstract

We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as expected from the Index Theorem, and their chirality expectation value is large (approximately 0.7). The remaining modes have low chirality and show clear signs of clustering into quartets and approaching the random matrix theory predictions for all topological charge sectors. We conclude that improvement of the fermionic and gauge actions moves the staggered quarks closer to the continuum limit where they respond correctly to QCD topology.