Diagonal Kenney-Laub Rational Approximation to the Overlap Dirac Operator

TL;DR

This paper introduces a practical lattice QCD method using diagonal Kenney-Laub rational approximations for the overlap Dirac operator, enhancing efficiency and chiral symmetry preservation.

Contribution

It presents a novel application of diagonal Kenney-Laub rational iterates for the overlap Dirac operator, improving computational efficiency and chiral symmetry in lattice QCD.

Findings

Improved chiral symmetry preservation with the new approximation.

Enhanced computational efficiency over Chebyshev polynomial methods.

Effective use of the Brillouin operator as kernel.

Abstract

We propose a practical formulation of the overlap Dirac operator in lattice QCD that employs the diagonal Kenney-Laub rational iterates - expressed via their partial fraction decomposition - to approximate the matrix sign function. We investigate this approximation using the Brillouin operator as kernel, in addition to the standard Wilson Dirac operator. Numerical results show improved chiral symmetry preservation and computational efficiency compared to the Chebyshev polynomial approach.