arXiv:2610.24074 · v2

QRecoupling.jl: numerical and exact computation of classical and quantum recoupling coefficients

QRecoupling.jl：经典与量子重耦合系数的数值与精确计算

首次提交 2026-10-17 02:01

版本更新 2026-11-10 02:49

雷达观测 2026-11-10 15:22

摘要

The Julia package QRecoupling evaluates classical and quantum recoupling coefficients, such as Clebsch-Gordan coefficients and $3j$ and $6j$ symbols, and user-defined sums of factorial products, with numerical, exact and symbolic targets. One compact factorial rule covers classical and deformed evaluations, while its cyclotomic exponents reveal common factors and determine which terms contribute at unitary levels. Adaptive arithmetic resolves strongly cancelling sums, while exact tests in quantum integers distinguish algebraic zeros from small nonzero values without a computer-algebra system. At spin cutoff 500, classical $3j$ and $6j$ symbols are evaluated about 7 and 15 times faster than with WIGXJPF. For the tested quantum deformations, relative errors remain below $4\times10^{-14}$ through spin cutoff 400. Recurrences compute fusion matrices with 401 channels about 100 times faster than loops over their entries. The resulting coefficients support recoupling identities, changes of coupling basis and tensor-network calculations.

作者备注：21 pages, 4 figures, 5 tables. Software: https://github.com/sethkasante/QRecoupling.jl (v0.6.4, doi:10.5281/zenodo.24027544)