Sparsening Algorithm for Multi-Hadron Lattice QCD Correlation Functions

TL;DR

This paper introduces a propagator sparsening algorithm for lattice QCD correlation functions that reduces computational costs while maintaining accurate extraction of ground-state properties in multi-hadron systems.

Contribution

The work presents a novel sparsening algorithm that constructs correlation functions from coarsened lattice propagators, enabling efficient calculations of multi-hadron systems in lattice QCD.

Findings

Ground state masses and binding energies are consistent between sparsened and full propagators.

The sparsening method reduces computational resources needed for correlation function calculations.

Modified couplings to excited states in sparsened correlation functions can be corrected inexpensively.

Abstract

Modern advances in algorithms for lattice QCD calculations have steadily driven down the resources required to generate gauge field ensembles and calculate quark propagators, such that, in cases relevant to nuclear physics, performing quark contractions to assemble correlation functions from propagators has become the dominant cost. This work explores a propagator sparsening algorithm for forming correlation functions describing multi-hadron systems, such as light nuclei, with reduced computational cost. The algorithm constructs correlation functions from sparsened propagators defined on a coarsened lattice geometry, where the sparsened propagators are obtained from propagators computed on the full lattice. This algorithm is used to study the low-energy QCD ground-state spectrum using a single Wilson-clover lattice ensemble with $m_{\pi} \approx 800$ MeV. It is found that the extracted ground state masses and binding energies, as well as their statistical uncertainties, are consistent when determined from correlation functions constructed from sparsened and full propagators. In addition, while evidence of modified couplings to excited states is observed in sparsened correlation functions, it is demonstrated that these effects can be removed, if desired, with an inexpensive modification to the sparsened estimator.