Rational r-matrices, higher rank Lie algebras and integrable proton–neutron BCS models Original Research Article

We study integrable cases of pairing BCS hamiltonians containing several types of fermions. We prove that there exist three classes of such integrable models associated with classical rational r-matrices and Lie algebras image, image and image correspondingly. We diagonalize the constructed hamiltonians by means of the algebraic Bethe ansatz. In the partial case of two types of fermions (image) the obtained models may be interpreted as image proton–neutron integrable models. In particular, in the case of image we recover the famous integrable proton–neutron model of Richardson.