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.

16 pages. v2: includes explicit expression for super-Yangian generator

References in corpus (3)

• Introduction to Yangian symmetry in integrable field theory
• Integrability of the russian doll BCS model
• The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity

Cited by in corpus (16)

• The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties
• Free fermions in disguise
• Free fermions behind the disguise
• Hidden string order in a hole-superconductor with extended correlated hopping
• The su(2|3) Undynamic Spin Chain
• Complexity of Supersymmetric Systems and the Cohomology Problem
• Free fermions beyond Jordan and Wigner
• Topological quantum pump of strongly interacting fermions in coupled chains
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
• A curious mapping between supersymmetric quantum chains
• Quantum circuits with free fermions in disguise
• Ground states of Nicolai and ${\mathbb{Z}}_2$ Nicolai models
• Exact real time dynamics with free fermions in disguise
• The Hilbert-space structure of free fermions in disguise
• BCS model with asymmetric pair scattering: a non-Hermitian, exactly solvable Hamiltonian exhibiting generalised exclusion statistics
• Local symmetries and extensive ground-state degeneracy of a 1D supersymmetric fermionic chain