All regular $4 \times 4$ solutions of the Yang-Baxter equation

Luke Corcoran, Marius de Leeuw

Published 2023-06-17Version 1

We complete the classification of $4\times 4$ 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.