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arXiv · 1207.4201

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

Kiaran B. Dave·Philip W. Phillips·Charles L. Kane
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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.

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Kiaran B. Dave, Philip W. Phillips, Charles L. Kane. 2012-07-17. Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function. https://doi.org/10.1103/physrevlett.110.090403

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