Improving the low-lying spectrum of the overlap kernel

TL;DR

This paper investigates the low-lying spectra of various overlap kernels to optimize the condition number, aiming to improve the computational efficiency of the overlap-Dirac operator in lattice QCD simulations.

Contribution

It provides an analysis of different kernels' spectra to identify candidates that reduce the condition number and accelerate overlap operator computations.

Findings

Certain kernels exhibit lower condition numbers, leading to faster overlap evaluations.

Spectral analysis guides the selection of more efficient kernels.

Potential for significant computational savings in lattice QCD calculations.

Abstract

The action of the overlap-Dirac operator on a vector is typically implemented in directly through a multi-shift conjugate gradient solver. The compute-time this takes to evaluate depends upon the condition number $\kappa$ of the matrix that is used as the overlap kernel. We examine the low-lying spectra of various candidate kernels in an effort to optimise $\kappa$, thereby speeding up the overlap evaluation.