A lattice Dirac operator for QCD with light dynamical quarks

TL;DR

This paper introduces a new approximately chiral lattice Dirac operator with a small residual mass, offering a computationally efficient alternative to existing fermion formulations for simulating light quarks in QCD.

Contribution

The authors develop and test a novel lattice Dirac operator based on Zolotarev rational approximation, achieving smaller residual mass than domain wall fermions at similar computational costs.

Findings

Smaller residual mass compared to domain wall fermions.

Maintains topological charge change capabilities.

Comparable performance in Hybrid Monte Carlo simulations.

Abstract

In QCD chiral symmetry is explicitly broken by quark masses, the effect of which can be described reliably by chiral perturbation theory. Effects of explicit chiral symmetry breaking by the lattice regularisation of the Dirac operator, typically parametrised by the residual mass, should be negligible for almost all observables if the residual mass of the Dirac operator is much smaller than the quark mass. However, maintaining a small residual mass becomes increasingly expensive as the quark mass decreases towards the physical value and the continuum limit is approached. We investigate the feasibility of using a new approximately chiral Dirac operator with a small residual mass as an alternative to overlap and domain wall fermions for lattice simulations. Our Dirac operator is constructed from a Zolotarev rational approximation for the matrix sign function that is optimal for bulk modes of the Hermitian kernel Dirac operator but not for the low-lying parts of its spectrum. We test our operator on various 32^3\times64 lattices, comparing the residual mass and the performance of the Hybrid Monte Carlo algorithm at a similar lattice spacing and pion mass with a hyperbolic tangent operator as used by domain wall fermions. We find that our approximations have a significantly smaller residual mass than domain wall fermions at a similar computational cost, and still admit topological charge change.