A modern Fortran library for SU(3) coupling and recoupling coefficients

TL;DR

This paper introduces a modern Fortran library for calculating SU(3) coupling and recoupling coefficients, improving accuracy and range over previous implementations, with applications in physics.

Contribution

A new Fortran library implementing algorithms for SU(3) coefficients, offering enhanced performance and broader quantum number support compared to existing tools.

Findings

Library supports larger SU(3) quantum numbers.

Provides more accurate coupling coefficients for large quantum numbers.

Outperforms the Akiyama-Draayer library in tests.

Abstract

The group $\mathrm{SU}(3)$ has applications in several branches of physics. Many of these applications depend on availability of $\mathrm{SU}(3)$ coupling and recoupling coefficients. We have developed a modern Fortran library for calculation of the coupling coefficients, for both the $\mathrm{SU}(3)\supset\mathrm{U}(1)\times\mathrm{SU}(2)$ and $\mathrm{SU}(3)\supset\mathrm{SO}(3)$ group chains, and the recoupling coefficients. The library implements the algorithms of Draayer, Akiyama, and Millener, which are laid out in the paper. Performance of the library has been tested and compared to the Akiyama-Draayer (AD) library implementing the same algorithms as well as to a more recent implementation. Our library works for a larger range of $\mathrm{SU}(3)$ quantum numbers and provides more accurate coupling coefficients with large quantum numbers than the AD library.