Diagonal Kenney-Laub Rational Approximation to the Overlap Operator using Wilson and Brillouin Kernel

Abstract

We propose a formulation of the overlap Dirac operator in lattice QCD that employs diagonal Kenney-Laub (KL) iterates to approximate the matrix sign function. KL iterates require no prior spectral information about the kernel operator and, when expressed via their partial fraction decomposition, offer a practical and efficient approximation scheme. We evaluate this approach in a proof-of-concept implementation using quenched lattices at $β=6.2$ and two Dirac operator discretizations as a kernel, namely the Wilson and the Brillouin operators. By examining the approximate overlap operator's violation of the Ginsparg-Wilson relation and the critical bare quark mass for increasing approximation order, we find that KL iterates deliver enhanced chiral symmetry preservation and computational efficiency compared to the Chebyshev polynomial approach.