Integrability of two-species partially asymmetric exclusion processes

We work towards the classification of all one-dimensional exclusion processes with two species of particles that can be solved by a nested coordinate Bethe ansatz (BA). Using the Yang-Baxter equations, we obtain conditions on the model parameters that ensure that the underlying system is integrable. Three classes of integrable models are thus found. Of these, two classes are well known in literature, but the third has not been studied until recently, and never in the context of the BA. The Bethe equations are derived for the latter model as well as for the associated dynamics encoding the large deviation of the currents.