New integrable 1D models of superconductivity

Abstract

In this paper we find new integrable one-dimensional lattice models of electrons. We describe all such nearest-neighbour integrable models with symmetry by classifying solutions of the Yang–Baxter equation following the procedure first introduced in []. We find 12 R-matrices of difference form, some of which can be related to known models such as the XXX spin chain and the free Hubbard model, and some are new models. In addition, integrable generalizations of the Hubbard model are found by keeping the kinetic term of the Hamiltonian and adding all terms which preserve fermion number. We find that most of the new models cannot be diagonalized using the standard nested Bethe Ansatz.