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

Abstract

We complete the classification of 4×4 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.