An Integrable Superconducting Model with Non-Fermi Liquid behavior

We study a model of a Superconductor whose normal state is a non-Fermi Liquid based on the Richardson-Gaudin Integrals of Motion. The resulting model that is integrable in all spatial dimensions, breaks a certain Z(2) symmetry that has been conjectured to be one of the key signatures of a Non-Fermi liquid. The non Superconducting ground state exhibits multiple Fermi surfaces, hence breaking Luttinger's theorem and, like the Hatsugai-Kohmoto model, has a macroscopically degenerate ground subspace. We present the Quantum Phase diagram of this model in 2 spatial dimensions, compare and contrast results from those obtained for the Hatsugai-Kohmoto model in the presence of mean field s-wave Superconducting terms.