Improving the Dirac Operator in Lattice QCD

TL;DR

This paper investigates new Dirac operators in lattice QCD that satisfy the Ginsparg-Wilson condition, analyzing their eigenvalue flow, stability, and efficiency on SU(3) gauge configurations with non-trivial topology.

Contribution

It compares the performance of a recently proposed chirally improved Dirac operator with other operators in terms of stability and efficiency in 4D lattice QCD.

Findings

Chirally improved operator shows favorable stability.

Eigenvalue flow analysis reveals topological features.

Efficiency varies among different Dirac operators.

Abstract

Recently various new concepts for the construction of Dirac operators in lattice Quantum Chromodynamics (QCD) have been introduced. These operators satisfy the so-called Ginsparg-Wilson condition (GWC), thus obeying the Atiyah-Singer index theorem and violating chiral symmetry only in a modest and local form. Here we present studies in 4-d for SU(3) gauge configurations with non-trivial topological content. We study the flow of eigenvalues and we compare the numerical stability and efficiency of a recently suggested chirally improved operator with that of others in this respect.