Integrability of an extended image-wave pairing Hamiltonian Original Research Article

We introduce an integrable Hamiltonian which is an extended image-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 image-wave pairing interactions through the mean-field analysis.