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

TL;DR

This paper completes the classification of regular 4x4 solutions to the Yang-Baxter equation, discovering four new models with non-trivial Jordan block structures, including a non-diagonalisable deformation of the XXX spin chain.

Contribution

It provides a complete classification of 4x4 regular solutions, adding four new non-difference form models with novel algebraic structures.

Findings

Four new models of non-difference form solutions identified

New models exhibit non-trivial Jordan block structures

One model is a non-diagonalisable deformation of the XXX spin chain

Abstract

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.