A new class of variance reduction techniques using lattice symmetries

TL;DR

This paper introduces a class of unbiased estimators using lattice symmetries that significantly reduces statistical errors in lattice gauge theory calculations, leading to substantial computational cost savings.

Contribution

It proposes covariant approximation averaging, a novel variance reduction technique leveraging lattice symmetry covariances, improving efficiency in physical observable computations.

Findings

Cost reductions of 16 times for nucleon mass calculations.

Cost reductions of 2.6-20 times for hadronic vacuum polarization.

Efficiency gains increase with decreasing quark mass and larger lattices.

Abstract

We present a general class of unbiased improved estimators for physical observables in lattice gauge theory computations which significantly reduces statistical errors at modest computational cost. The error reduction techniques, referred to as covariant approximation averaging, utilize approximations which are covariant under lattice symmetry transformations. We observed cost reductions from the new method compared to the traditional one, for fixed statistical error, of 16 times for the nucleon mass at $M_\pi\sim 330$ MeV (Domain-Wall quark) and 2.6-20 times for the hadronic vacuum polarization at $M_\pi\sim 480$ MeV (Asqtad quark). These cost reductions should improve with decreasing quark mass and increasing lattice sizes.