Luttinger's theorem in the presence of Luttinger surfaces

Abstract

Breakdown of Landau's hypothesis of adiabatic continuation from noninteracting 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 realization of a spin-liquid insulator.