Novel Algorithms for Computing Nuclear Correlation Functions in Lattice Quantum Chromodynamics

Abstract

Techniques to attain numerical solutions of Quantum Chromodynamics have developed to the point of beginning to connect aspects of nuclear physics to the underlying degrees of freedom of the Standard Model. There remain deep physical and numerical challenges, including a proliferation of possibilities for interpolating operators that couple to low-energy states, factorial numerical resource scaling, poor signal-to-noise scaling, and potentially dominating floating-point precision errors. The focus of this work is the computational resource scaling associated with numerically evaluating the correlation function for an interpolating operator possessing the quantum numbers of a multi-baryon system in the context of lattice QCD. The naïve computational cost required to compute nuclear correlation functions grows factorially in the number of quarks, however this work develops a set of novel approaches that reduce this cost by exploiting inherent permutation symmetry. A selection of benchmarks demonstrate that the new methods can offer between one and two orders of magnitude in reduced calculation time (excluding hadron block expression evaluation) for correlation functions of light nuclei when compared against the hadron block method alone.