Reply to the Comments by B. Farid and A.M. Tsvelik, arXiv:0909.2886v1, and B. Farid, arXiv:0909.2887v1

TL;DR

This paper defends previous conclusions on the violation of the Luttinger sum rule in certain models, arguing that recent comments disputing these conclusions are unconvincing, but the fundamental question remains open.

Contribution

It provides a rebuttal to recent critiques of earlier work on the Luttinger sum rule violations in specific strongly correlated models.

Findings

Arguments against the original analysis are easily rejected.

The validity and breakdown of the Luttinger sum rule still require further investigation.

Abstract

In the recent preprints the authors claim that conclusions on the violation of the Luttinger sum rule (LSR) as put forward in published papers by the present authors are false or at least not conclusive enough. It concerns the validity of the LSR within the Mott-Hubbard insulator as manifested in the 1D model of spinless fermions, and the Hubbard model on a triangular lattice. We show below that arguments against the presented analysis are rather easily rejected while still the general question of the validity and breakdown of the LSR remains to be answered.