Classifying integrable spin-1/2 chains with nearest neighbour interactions

Abstract

We classify all fundamental integrable spin chains with two-dimensional (2D) local Hilbert space which have regular R-matrices of difference form. This means that the R-matrix underlying the integrable structures is of the form and reduces to the permutation operator at some particular point. We find a total of 14 independent solutions, eight of which correspond to well-known eight or lower vertex models. The remaining six models appear to be new and some have peculiar properties such as not being diagonalizable or being nilpotent. Furthermore, for even R-matrices, we find a bijection between solutions of the Yang–Baxter equation (YBE) and the graded YBE which extends our results to the graded 2D case.