Exact solution of the p+ip Hamiltonian revisited: duality relations in the hole-pair picture

TL;DR

This paper revisits the exact Bethe Ansatz solution of the p+ip Hamiltonian, highlighting duality relations in the hole-pair framework and revealing asymmetries with the particle-pair approach, especially in the strong pairing regime.

Contribution

It introduces a hole-pair based formulation of the Bethe Ansatz solution, uncovering asymmetries and novel features in the strong pairing regime of the p+ip Hamiltonian.

Findings

States form a quasi-condensate involving two hole-pair operators in the strong pairing regime

Asymmetry observed between hole-pair and particle-pair descriptions

Hole-pair picture reveals duality relations not seen in particle-pair approach

Abstract

We study the exact Bethe Ansatz solution of the p+ip Hamiltonian in a form whereby quantum numbers of states refer to hole-pairs, rather than particle-pairs used in previous studies. We find an asymmetry between these approaches. For the attractive system states in the strong pairing regime take the form of a quasi-condensate involving two distinct hole-pair creation operators. An analogous feature is not observed in the particle-pair picture.