• DOI:10.1103/PhysRevLett.110.090403
• Corpus ID: 1134967

Absence of Luttinger's theorem due to zeros in the single-particle Green function.

@article{Dave2013AbsenceOL,
  title={Absence of Luttinger's theorem due to zeros in the single-particle Green function.},
  author={Kiaran B. Dave and Philip W. Phillips and Charles L. Kane},
  journal={Physical review letters},
  year={2013},
  volume={110 9},
  pages={
          090403
        }
}

• K. B. Dave, P. Phillips, C. Kane
• Published 17 July 2012
• Mathematics
• Physical review letters

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(T→0), 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.