Comment on "Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice", by J. Kokalj and P. Prelovsek [Eur. Phys. J. B 63, 431 (2008), arXiv:arXiv:0709.0263]

TL;DR

This paper critiques a previous study claiming a breakdown of the Luttinger theorem in a Hubbard model on a triangular lattice, showing that the observed violation is an artifact of a first-order approximation and not a fundamental failure.

Contribution

The authors demonstrate that the reported violation of the Luttinger theorem is an artifact of first-order series expansion, clarifying the conditions under which the theorem holds.

Findings

First-order expansion falsely indicates Luttinger theorem violation.

Violation occurs only when mu' ≠ 0, not at mu' = 0.

The original claim is an artifact of approximation, not a fundamental breakdown.

Abstract

Using the first-order series expansion of the function G(k;mu), in powers of mu' = mu - U/2, pertaining to the insulating ground state of a single-band Hubbard Hamiltonian at half-filling, Kokalj and Prelovsek have in a recent paper [Eur. Phys. J. B 63, 431 (2008), arXiv:arXiv:0709.0263] reported breakdown of the Luttinger theorem for the specific case where the lattice on which the Hubbard Hamiltonian is defined is a two-dimensional triangular lattice, for which the ground state is not invariant under particle-hole transformation. Here G(k;mu) is the single-particle Green function G(k;e) evaluated at e = mu, the zero-temperature limit of the chemical potential corresponding to half-filling, and U the on-site interaction energy. In this Comment we demonstrate that unless mu' = 0 (to be strictly distinguished from mu' small but non-vanishing), any finite-order series expansion for G(k;mu) in powers of mu' in general falsely signals breakdown of the Luttinger theorem. The violation of this theorem as asserted by Kokalj and Prelovsek is therefore an artifact of their first-order calculation.