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

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 similar to 100 for the point-source operator and a factor of similar to 1000 for the Gaussian-smeared operator, while the uncertainties of the correlators only increase by similar to 15%. Therefore, with a modest cost of the computational resources, one can approach the precision of the ail-to-all correlators using the field-sparsening methods.

Automated summary

Two field-sparsening methods, the sparse-grid method and the random field selection method, are utilized in this study to construct 2-point and 3-point correlation functions in lattice QCD. By summing over a subset of lattice sites due to high correlation among different field points, computational time can be significantly saved. The reduction in field points for point-source and Gaussian-smeared operators leads to only a slight increase in uncertainties of the correlators, allowing for approaching the precision of ail-to-all correlators with modest computational resources cost.