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 \cite{ deLeeuw:2019zsi}. 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 $16\times 16$ solutions which exhibit $\mathfrak{ su}(2)\oplus \mathfrak{ su}(2)$ symmetry, which include the one-dimensional Hubbard model and the $S$-matrix of the ${ \rm AdS}_5 \times { \rm S}^5$ superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.
Categories: math-ph cond-mat.stat-mech hep-th math.MP nlin.SI