1207.4201 (Kiaran B. Dave et al.)

Absence of Luttinger's Theorem    [PDF]

Kiaran B. Dave, Philip W. Phillips, Charles L. Kane

We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, $\mu$, for a T=0 gapped system is removed by using the unique value $\mu(T\rightarrow 0)$, Luttinger's sum rule is violated. The failure stems from the non-existence 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 elemental particle picture in strongly correlated electron matter.

View original: http://arxiv.org/abs/1207.4201