Field sparsening for the construction of the correlation functions in lattice QCD

TL;DR

This paper introduces field-sparsening techniques in lattice QCD to significantly reduce computational costs in constructing correlation functions while maintaining high accuracy, by exploiting correlations among lattice points.

Contribution

It presents two novel field-sparsening methods that drastically decrease the number of lattice points needed for correlation functions without substantial loss of precision.

Findings

Field points reduced by factors of 100 and 1000 for different operators.

Correlator uncertainties increase by only ~15%.

Approaches all-to-all correlator precision at modest computational cost.

Abstract

Two field-sparsening methods, namely the sparse-grid method and the random field selection method, are used in this paper for the construction of the 2-point and 3-point correlation functions in lattice QCD. We argue that, due to the high correlation among the lattice correlators at different field points associated with source, current, and sink locations, one can save a lot of computational time by performing the summation over a subset of the lattice sites. Furthermore, with this strategy, one only needs to store a small fraction of the full quark propagators. It is found that the number of field points can be reduced by a factor of $\sim$100 for the point-source operator and a factor of $\sim$1000 for the Gaussian-smeared operator, while the uncertainties of the correlators only increase by $\sim$15\%. Therefore, with a modest cost of the computational resources, one can approach the precision of the all-to-all correlators using the field-sparsening methods.