Theory of the Luttinger surface in doped 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 noninteracting system. Such a divergence gives rise to a surface of zeros ͑the Luttinger surface͒ 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 noninteracting limit. A modified version of Luttinger's theorem is derived for special cases.

First-order Mott transition at zero temperature in two dimensions: Variational plaquette study

“…For K = (π, 0) and K = (0, π) the transition is of the Mott-Hubbard type. This is consistent with the fact that for the particle-hole symmetric case and in the Mott-insulating state, the selfenergy at ω = 0 diverges on the non-interacting Fermi surface [27]. For K = (0, 0) and K = (π, π), the insulating spectral function is neither Mott-Hubbard-like (as it is not particle-hole symmetric) nor band-insulator-like (as the "orbital" K = (0, 0) is not fully occupied and the "orbital" K = (π, π) not completely empty).…”

Determining the underlying Fermi surface of strongly correlated superconductors

“…In the Fermi liquid state of normal metals, the Luttinger surface coincides with the FS. In a Mott-Hubbard insulator the Green's function changes sign because of a characteristic 1͞ divergence of the single-particle self-energy (13,14) at momenta k of the noninteracting FS. In the HTSC the gapped states destroy the FS but only mask the Luttinger surface.…”

Absence of Luttinger’s Theorem due to Zeros in the Single-Particle Green Function

“…(1) reduces exactly to n = 2Θ(0) = 1, a result which holds beyond the atomic limit [11]. Farid's claim is interesting then because it would seem to establish a rigorous relationship between a quantity which has no obvious physical import and a conserved one, the particle density.…”

“…(1) portends for strongly interacting electron systems is that although the degrees of freedom that give rise to zeros undoubtedly contribute to the current, they have no bearing on the particle density. The particle density is determined by coherence (ℑΣ < ǫ) while zeros arise from incoherence ( ℑΣ diverges [11] signifying that there is no particle to contribute to n). As a result, there exist charged degrees of freedom in strongly correlated electron matter which couple to the current but nonetheless cannot be given an interpretation in terms of elemental fields.…”