Index Theorem and Random Matrix Theory for Improved Staggered Quarks

TL;DR

This paper demonstrates that improved staggered quark operators in lattice QCD accurately reflect topological features and align with random matrix theory predictions, indicating progress towards the continuum limit.

Contribution

It shows that improved staggered quarks exhibit correct topological behavior and spectral clustering consistent with continuum QCD and random matrix theory.

Findings

Eigenvalue spectra separate into zero modes and others.

Zero modes correspond to topological charge with large chirality.

Remaining modes cluster into quartets and match RMT 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 of eigenvalues 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. 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.