All regular 4 × 4 solutions of the Yang-Baxter equation

2023/06/17 by Corcoran, Luke, de Leeuw, Marius
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2306.10423

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.

Related

• All 4 x 4 solutions of the quantum Yang-Baxter equation
• Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation
• Solution of Constant Yang-Baxter System in the Dimension Two
• Integrable lattice models from four-dimensional field theories
• Solutions to the matrix Yang-Baxter equation