Cooper pairs and exclusion statistics from coupled free-fermion chains

Abstract

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 Haldane-Shastry 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 infinite-dimensional symmetry algebra, which is a supersymmetric version of the Yangian symmetry algebra for the Haldane-Shastry model.