Absence of Luttinger’s Theorem due to Zeros in the Single-Particle Green Function
Kiaran B. Dave, Philip Phillips, C. L. Kane
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.
arXiv:1207.4201•Physical Review Letters•Feb 28, 2013•69 citations