All regular $4 \times 4$ solutions of the Yang-Baxter equation
High Energy Physics - Theory
2024-02-22 v3 Statistical Mechanics
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We complete the classification of regular solutions of the Yang-Baxter equation. Apart from previously known models, we find four new models of non-difference form. All the new models give rise to Hamiltonians and transfer matrices that have a non-trivial Jordan block structure. One model corresponds to a non-diagonalisable integrable deformation of the XXX spin chain.
Keywords
Cite
@article{arxiv.2306.10423,
title = {All regular $4 \times 4$ solutions of the Yang-Baxter equation},
author = {Luke Corcoran and Marius de Leeuw},
journal= {arXiv preprint arXiv:2306.10423},
year = {2024}
}
Comments
18 pages. v2: references added. v3: typos corrected/references added