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Luttinger's theorem in presence of Luttinger surfaces

Breakdown of Landau's hypothesis of adiabatic continuation from non-interacting to fully interacting electrons is commonly believed to bring about a violation of Luttinger's theorem. Here, we elucidate what may go wrong in the proof of Luttinger's theorem. The analysis provides a simple way to correct Luttinger's expression of the electron number in single-band models where perturbation theory breaks down through the birth of a Luttinger surface without symmetry breaking. In those cases, we find that the Fermi volume only accounts for the doping away from half-filling. In the hypothetical circumstance of a non-symmetry breaking Mott insulator with a Luttinger surface, our analysis predicts the noteworthy existence of quasiparticles whose `Fermi` surface is just the Luttinger one. Therefore, those quasiparticles can be legitimately regarded as `spinons`, and the Mott insulator with a Luttinger surface as realisation of a spin-liquid insulator.