Aspects of Propagator Sparsening in Lattice QCD

TL;DR

This paper explores a new covariant averaging method for propagator sparsening in lattice QCD, improving the efficiency of calculations while preserving essential physical correlations.

Contribution

It introduces a covariant averaging approach to propagator sparsening and demonstrates its effectiveness in maintaining correlation functions in lattice QCD.

Findings

Covariant averaging enhances sparsening effectiveness.

Sequential averaging best preserves correlation functions.

Method reduces computational costs while maintaining physics fidelity.

Abstract

In lattice field theory, field sparsening aims to replace quantum fields, or objects constructed from them, with approximations that preserve the appropriate symmetries and maintain many aspects of the physics that the fields determine. For example, an effective sparsening of a quark propagator provides an efficient map from a quark propagator on a fine lattice geometry to a quark propagator defined on a coarser geometry in order to reduce storage and computational costs of subsequent calculational stages while maintaining long-distance correlations and corresponding low-energy physical information. Previous studies have focused on decimating lattice sites or randomly sampling lattice sites to reduce the size of the propagator and subsequent costs of Wick contractions. Here, we extend the study of sparsening to incorporate covariant averaging of spatial sites and examine the effects on two-point and three-point correlation functions involving various hadrons. We find that sparsening is most effective in reproducing the unsparsened versions of these correlation functions when weighted covariant-averaging is sequentially applied many times.