Violation of Luttinger's theorem in strongly correlated electronic systems within a 1/N expansion

TL;DR

This paper investigates the 1/N expansion of a strongly correlated electron model, revealing that Luttinger's theorem is violated at next-to-leading order, with implications for Fermi surface volume and self-energy calculations.

Contribution

It demonstrates the violation of Luttinger's theorem in a 1/N expansion of the SU(N) Hubbard model and provides an explicit O(1/N) self-energy expression with vertex corrections.

Findings

Fermi liquid behavior at leading order

Violation of Luttinger's theorem at next-to-leading order

Explicit O(1/N) self-energy expression with vertex corrections

Abstract

We study the 1/N expansion of a generic, strongly correlated electron model (SU(N) symmetric Hubbard model with $U=\infty$ and N degrees of freedom per lattice site) in terms of X operators. The leading order of the expansion describes a usual Fermi liquid with renormalized, stable particles. The next-to-leading order violates Luttinger's theorem if a finite convergence radius for the 1/N expansion for a fixed and non-vanishing doping away from half-filling is assumed. We find that the volume enclosed by the Fermi surface, is at large, but finite N's and small dopings larger than at $N=\infty$. As a by-product an explicit expression for the electronic self-energy in O(1/N) is given which cannot be obtained by factorization or mode-coupling assumptions but contains rather sophisticated vertex corrections.