Comment on `On the Luttinger theorem concerning the number of particles in the ground states of systems of interacting fermions', arXiv:0711.0952v1, by B. Farid

TL;DR

This paper critiques Farid's claim that the Luttinger theorem applies to Mott insulators when the chemical potential is defined at zero temperature, arguing that particle-hole asymmetry can violate the theorem.

Contribution

The authors challenge Farid's assertion by demonstrating that particle-hole asymmetry can lead to violations of the Luttinger theorem in Mott insulators.

Findings

Luttinger theorem can be violated in particle-hole asymmetric Mott insulators.

Weak particle-hole symmetry breaking does not necessarily destroy the Mott insulating state.

Farid's argument about the universality of the theorem in such systems is contested.

Abstract

In his preprint, arXiv:0711.0952v1, Behnam Farid argues that the Luttinger theorem is valid not only for a metal but also for a Mott insulator if the chemical potential is calculated by taking the limit of vanishing temperature at fixed particle density. In contrast, we have found in our recent paper (Eur. Phys. J. B 59, 495 (2007) or arXiv:cond-mat/0602656) on the basis of a controlled strong coupling expansion that the Luttinger theorem is violated in this limit for a particle-hole asymmetric two-band Mott insulator. In an extensive discussion of our result Farid argues that an arbitrarily weak breaking of particle-hole symmetry leads to a destruction of the Mott insulating state at half filling. In this comment we point out that this is not correct.