All 4 x 4 solutions of the quantum Yang-Baxter equation

Abstract

In this paper, we complete the classification of 4 x 4 solutions of the Yang-Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions, then consider regular and non-regular Lax operators and study their relation to the quantum Yang-Baxter equation. We show that for regular solutions there is a correspondence, which is lost in the non-regular case. In particular, we find non-regular Lax operators whose R-matrix from the fundamental commutation relations is regular but does not satisfy the Yang-Baxter equation. These R-matrices satisfy a modified Yang-Baxter equation instead.

arXiv commentv6: changed title

References in corpus (12)

• How Algebraic Bethe Ansatz works for integrable model
• Geometry and classification of solutions of the Classical Dynamical Yang-Baxter Equation
• The complete solution to the constant quantum Yang-Baxter equation in two dimensions
• Yang-Baxter and the Boost: splitting the difference
• Classifying nearest-neighbour interactions and deformations of AdS
• Classifying integrable spin-1/2 chains with nearest neighbour interactions
• Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems
• Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras
• Generalized Yang-Baxter Equation
• Boundary solutions of the quantum Yang-Baxter equation and solutions in three dimensions
• New spectral-parameter dependent solutions of the Yang-Baxter equation
• On Solutions to the Twisted Yang-Baxter equation