Much Ado about Zeros: The Luttinger Surface and Mottness

TL;DR

This paper demonstrates that Mott insulators are characterized by a divergence in the electron self energy at specific momenta, leading to a surface of zeros in the Green function, which unifies various phenomena in doped Mott insulators.

Contribution

It establishes the existence of a Luttinger surface of zeros in Mott insulators and links it to Mottness, pseudogap phenomena, and spectral features, extending Luttinger's theorem.

Findings

Divergence of self energy at specific momenta in Mott insulators.

Presence of a Luttinger surface of zeros in the Green function.

Breakdown of traditional Luttinger's theorem in Mott insulators.

Abstract

We prove that the Mott insulating state is characterized by a divergence of the electron self energy at well-defined values of momenta in the first Brillouin zone. When particle-hole symmetry is present, the divergence obtains at the momenta of the Fermi surface for the corresponding non-interacting system. Such a divergence gives rise to a surface of zeros (the Luttinger surface) of the single-particle Green function and offers a single unifying principle of Mottness from which pseudogap phenomena, spectral weight transfer, and broad spectral features emerge in doped Mott insulators. We also show that only when particle-hole symmetry is present does the volume of the zero surface equal the particle density. We identify that the general breakdown of Luttinger's theorem in a Mott insulator arises from the breakdown of a perturbative expansion for the self energy in the single-particle Green function around the non-interacting limit. A modified version of Luttinger's theorem is derived for special cases.