BCS model with asymmetric pair scattering: a non-Hermitian, exactly solvable Hamiltonian exhibiting generalised exclusion statistics

TL;DR

This paper presents an exactly solvable non-Hermitian BCS model with asymmetric pair scattering, revealing free quasi-particles obeying generalized exclusion statistics through algebraic Bethe ansatz and Yangian algebra.

Contribution

It introduces a novel non-Hermitian BCS Hamiltonian with asymmetric scattering, solved exactly using algebraic Bethe ansatz, and uncovers quasi-particles obeying generalized exclusion statistics.

Findings

Exact solution of the non-Hermitian BCS model.

Identification of quasi-particles obeying generalized exclusion statistics.

Connection between Yangian algebra and the model's excitations.

Abstract

We demonstrate the occurrence of free quasi-particle excitations obeying generalised exclusion statistics in a BCS model with asymmetric pair scattering. The results are derived from an exact solution of the Hamiltonian, which was obtained via the algebraic Bethe ansatz utilising the representation theory of an underlying Yangian algebra. The free quasi-particle excitations are associated to highest-weight states of the Yangian algebra, corresponding to a class of analytic solutions of the Bethe ansatz equations.