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
        }
}
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… 

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