Classifying Nearest-Neighbor Interactions and Deformations of AdS

Abstract

We classify all regular solutions of the Yang-Baxter equation of eight-vertex type. Regular solutions correspond to spin chains with nearest-neighbor interactions. We find a total of four independent solutions. Two are related to the usual six-and eight-vertex models that have R matrices of difference form. We find two new solutions of the Yang-Baxter equation, which are manifestly of nondifference form. These new solutions contain the S-matrices of the AdS2 and AdS3 integrable models as a special case. This can be used as a starting point to study and classify integrable deformations of these holographic integrable systems.