Nuclear correlation functions using first-principle calculations of lattice quantum chromodynamics

Abstract

Exploring nuclear physics through the fundamental constituents of the strong force -- quarks and gluons -- is a formidable challenge. While numerical calculations using lattice quantum chromodynamics offer the most promising approach for this pursuit, practical implementation is arduous, especially due to the uncontrollable growth of quark-combinatorics, the so-called Wick-contraction problem of nuclei. We present here two novel methods providing a state-of-the-art solution to this problem. In the first, we exploit randomized algorithms inspired from computational number theory to detect and eliminate redundancies that arise in Wick contraction computations. Our second method explores facilities for automation of tensor computations -- in terms of efficient utilization of specialized hardware, algorithmic optimizations, as well as ease of programming and the potential for automatic code generation -- that are offered by new programming models inspired by applications in machine learning (e.g., TensorFlow). We demonstrate the efficacy of our methods by computing two-point correlation functions for Deuteron, Helium-3, Helium-4 and Lithium-7, achieving at least an order of magnitude improvement over existing algorithms with efficient implementation on GPU-accelerators. Additionally, we discover an intriguing characteristic shared by all the nuclei we study: specific spin-color combinations dominate the correlation functions, hinting at a potential connection to an as-yet-unidentified symmetry in nuclei. Moreover finding them beforehand can reduce the computing time further and substantially. Our results, with the efficiency that we achieved, suggest the possibility of extending the applicability of our methods for calculating properties of light nuclei, potentially up to A ~12 and beyond.

68 pages with 6 tables and 23 figures including an Appendix. To be published in Physical Review D

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