Higher-order hopping-parameter expansion by human-AI collaboration

Abstract

We develop efficient algorithms for evaluating higher-order terms in the hopping-parameter expansion of $\text{Tr}\ln M$ on $SU(N_{\text{c}})$ gauge configurations. The resulting algorithms, which exploit a trie data structure for the computation of high-order terms, evaluate the ${\kappa }^8$, ${\kappa }^{10}$, and ${\kappa }^{12}$ terms at computational costs of approximately $20$, $460$, and $8900$ times that of a single staple evaluation, respectively. The correctness of the algorithms is verified by comparison with a computationally expensive but reliable reference calculation. We emphasize that collaboration between human researchers and AI coding agents was essential to the development of these algorithms.

7 pages, 1 figure, Substantial revision, including major algorithmic improvements