Luttinger sum rule for finite systems of correlated electrons

TL;DR

This paper investigates the validity of the Luttinger sum rule in finite correlated electron systems, revealing violations in the t-J model at low doping but not conclusively in the Hubbard model.

Contribution

It provides a comparative analysis of the Luttinger sum rule's applicability in finite t-J and Hubbard models, highlighting conditions of violation.

Findings

Luttinger sum rule is violated in the t-J model at low doping.

No definitive violation found in the Hubbard model with next-nearest-neighbor hopping.

The sum rule's validity depends on the specific model and doping level.

Abstract

The validity of the Luttinger sum rule is considered for finite systems of interacting electrons, where the Fermi volume is determined by location of zeroes of Green's function. It is shown that the sum rule in the paramagnetic state is evidently violated within the planar t-J model at low doping while for the related Hubbard model, even in the presence of next-nearest-neighbor hopping, no clearcut exception is found.