Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice

TL;DR

This paper investigates the validity of the Luttinger sum rule in a Hubbard model on a triangular lattice, revealing significant violations in a specific strongly correlated electron system.

Contribution

It develops a frequency-moment expansion method to analyze the Luttinger sum rule in the Hubbard model at half filling and large U, highlighting violations on a triangular lattice.

Findings

Significant violation of the Luttinger sum rule on a triangular lattice

Methodology based on frequency-moment expansion

Results specific to the Hubbard model with nearest-neighbor hopping

Abstract

The frequency-moment expansion method is developed to analyze the validity of the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the generalized Hubbard model at half filling and large $U$. For the particular case of the Hubbard model with nearest-neighbor hopping on a triangular lattice lacking the particle-hole symmetry results reveal substantial violation of the sum rule.