Unified contraction algorithm for multi-baryon correlators on the lattice

TL;DR

The paper introduces a unified algorithm for calculating multi-baryon correlation functions on the lattice, significantly reducing computational costs by eliminating redundancies through simultaneous permutation and contraction considerations.

Contribution

A novel unified contraction algorithm that reduces computational costs for multi-baryon correlators on the lattice by considering permutations and contractions simultaneously.

Findings

Achieved up to 192-fold reduction for $^3$H and $^3$He nuclei.

Achieved up to 20736-fold reduction for $^4$He nucleus.

Extensions applicable to systems with hyperons.

Abstract

We propose a novel algorithm for calculating multi-baryon correlation functions on the lattice. By considering the permutation of quarks (Wick contractions) and color/spinor contractions simultaneously, we construct a unified index list for the contraction where the redundancies in the original contraction are eliminated. We find that a significant reduction in the computational cost of correlators is achieved, e.g., by a factor of 192 for $^3$H and $^3$He nuclei, and a factor of 20736 for the $^4$He nucleus, without assuming isospin symmetry. A further reduction is possible by exploiting isospin symmetry, and/or interchange symmetries associated with sink baryons, if such symmetries exist. Extensions for systems with hyperons are presented as well.