Integrability of an extended d+id-wave pairing Hamiltonian

TL;DR

This paper introduces an exactly solvable extended d+id-wave pairing Hamiltonian, analyzing its properties through Bethe ansatz, continuum limit, and mean-field approaches, revealing gapless excitations and connections to non-integrable models.

Contribution

It presents a new integrable d+id-wave pairing model derived from a duality with the Richardson-Gaudin s-wave model, providing exact solutions and analysis methods.

Findings

Exact Bethe ansatz solution for the extended d+id-wave model

Identification of gapless excitation spectra in certain regimes

Demonstration of consistency between continuum limit and mean-field results

Abstract

We introduce an integrable Hamiltonian which is an extended d+id-wave pairing model. The integrability is deduced from a duality relation with the Richardson-Gaudin (s-wave) pairing model, and associated to this there exists an exact Bethe ansatz solution. We study this system using the continuum limit approach and solve the corresponding singular integral equation obtained from the Bethe ansatz solution. We also conduct a mean-field analysis and show that results from these two approaches coincide for the ground state in the continuum limit. We identify instances of the integrable system where the excitation spectrum is gapless, and discuss connections to non-integrable models with d+id-wave pairing interactions through the mean-field analysis.