Luttinger's theorem in presence of Luttinger surfaces

TL;DR

This paper revises Luttinger's theorem for systems with Luttinger surfaces, showing how to correctly account for electron count and quasiparticles in strongly correlated insulators without symmetry breaking.

Contribution

It identifies the failure points in the traditional proof of Luttinger's theorem and proposes a corrected expression applicable to models with Luttinger surfaces, linking them to spin-liquid insulators.

Findings

Luttinger's theorem needs correction in presence of Luttinger surfaces.

The Fermi volume accounts only for doping in such systems.

Existence of spinon-like quasiparticles with Luttinger surfaces in Mott insulators.

Abstract

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.