Cooper pairs and exclusion statistics from coupled free-fermion chains

TL;DR

This paper introduces a model of coupled free-fermion chains that produces zero-energy Cooper pairs and particles obeying exclusion statistics, solved exactly via nested Bethe ansatz, revealing a supersymmetric Yangian symmetry.

Contribution

It presents a novel exactly solvable model coupling free-fermion chains with Cooper pairs and exclusion statistics, exhibiting a supersymmetric Yangian symmetry.

Findings

Exact solutions for all eigenstates using nested Bethe ansatz

Identification of Cooper pairs as zero-energy solutions

Discovery of an infinite-dimensional supersymmetric symmetry algebra

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.