Classical r-matrices and integrable BCS models with many types of fermions

Abstract

Based on generalized Gaudin models and Lie algebras so(2m), we construct two integrable cases of the pairing BCS Hamiltonians containing m types of ‘spinless’ fermions. They are the so-called s-type and px + ipy-type BCS Hamiltonians. In the particular case of the Lie algebra so(8), the constructed models can be viewed as N = Z proton–neutron integrable models. We find the spectrum of the constructed Hamiltonians in terms of solutions of Bethe-type equations.