The Low-Lying Dirac Spectrum of Staggered Quarks

TL;DR

This paper studies the low-lying Dirac spectrum of staggered quarks in lattice QCD, demonstrating correct topological responses and consistency with theoretical predictions when using improved actions.

Contribution

It clarifies the role of topology in staggered quarks and shows improved actions correctly reproduce continuum topological features.

Findings

Spectrum separates into zero modes and others as predicted

Number of zero modes matches topological charge via Index Theorem

Eigenvalue distributions agree with random matrix theory

Abstract

We investigate and clarify the role of topology and the issues surrounding the epsilon regime for staggered quarks. We study unimproved and improved staggered quark Dirac operators on quenched lattice QCD gluon backgrounds generated using a Symanzik-improved gluon action. For the improved Dirac operators 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 predicted by the continuum Index Theorem, and the expectation values of their chirality are large for the most improved actions (approx 0.7). The remaining modes have low chirality and show clear signs of clustering into quartets that become degenerate in the continuum limit. We demonstrate that the lattice spacing and volume dependence of the eigenvalues follow expectations. Furthermore, the non-zero modes follow the random matrix theory predictions for all topological charge sectors. The values of the chiral condensate extracted from fits to the theoretical distributions are consistent with each other, and with the results obtained from the total density of eigenvalues using the Banks-Casher relation. We conclude that staggered quarks respond correctly to QCD topology when both fermion and gauge actions are improved.