Cooper pairs and exclusion statistics from coupled free - fermion chains

We show how to couple two free-fermion chains so that the excitations consist of Cooper pairs with zero energy, and free particles obeying (mutual) exclusion statistics. This behavior is reminiscent of anyonic superconductivity, and of a ferromagnetic version of the HaldaneShastry spin chain, although here the interactions are local. We solve this model using the nested Bethe ansatz, and find all the eigenstates; the Cooper pairs correspond to exact-string or “0/0” solutions of the Bethe equations. We show how the model possesses an infinitedimensional symmetry algebra, which is a supersymmetric version of the Yangian symmetry algebra for the Haldane-Shastry model.