title: Absence of Luttinger's theorem due to zeros in the single-particle Green function.
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(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.
authors.affiliation: Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801, USA.
authors.forename: Kiaran B
authors.initials: KB
authors.lastname: Dave
authors.forename: Philip W
authors.initials: PW
authors.lastname: Phillips
authors.forename: Charles L
authors.initials: CL
authors.lastname: Kane