Yang-Baxter and the Boost: splitting the difference

Abstract

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in [1]. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16\times1616×16 solutions which exhibit \mathfrak{su}(2)\oplus \mathfrak{su}(2)𝔰𝔲(2)⊕𝔰𝔲(2) symmetry, which include the one-dimensional Hubbard model and the SS-matrix of the {AdS}_5 \times {S}^5AdS5×S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.