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

Kiaran B. Dave, Philip W. Phillips, and Charles L. Kane
Phys. Rev. Lett. 110, 090403 – Published 28 February 2013
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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, μ, for a T=0 gapped system is removed by using the unique value μ(T0), Luttinger’s sum rule is violated even if the ground-state degeneracy is lifted by an infinitesimal hopping. The failure stems from the nonexistence 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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  • Received 26 July 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.090403

© 2013 American Physical Society

Authors & Affiliations

Kiaran B. Dave and Philip W. Phillips

  • Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801, USA

Charles L. Kane

  • Department of Physics and Astonomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

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Vol. 110, Iss. 9 — 1 March 2013

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