Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function

TL;DR

This paper demonstrates that Luttinger's theorem fails in certain strongly correlated systems due to divergences in the self-energy, supported by theoretical models and experimental data on cuprates, indicating a breakdown of quasiparticle descriptions.

Contribution

It provides an exact demonstration that Luttinger's theorem does not hold in specific SU(N) models with diverging self-energy, challenging conventional quasiparticle-based theories.

Findings

Luttinger's sum rule is violated in the model despite removing chemical potential ambiguity.

The Luttinger-Ward functional does not exist when the self-energy diverges.

Experimental data on cuprates show deviations from Luttinger count, indicating breakdown of quasiparticle picture.

Abstract

We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, $\mu$, for a T=0 gapped system is removed by using the unique value $\mu(T\rightarrow 0)$, Luttinger's sum rule is violated even if the ground-state degeneracy is lifted by an infinitesimal hopping. The failure stems from the non-existence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger's theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists. Experimental data on the cuprates are presented which show a systematic deviation from the Luttinger count, implying a breakdown of the electron quasiparticle picture in strongly correlated electron matter.