Response to Greiter's Comment

TL;DR

This paper corrects a misconception about the energy of pi-excitations in the Hubbard model, emphasizing the importance of consistent treatment of Hartree energies and clarifying the interpretation of finite-size studies.

Contribution

It clarifies the correct energy scale of pi-excitations in the Hubbard model and addresses misconceptions in previous finite-size analyses.

Findings

Hartree energy and chemical potential corrections cancel in self-consistent calculations

Greiter's interpretation of finite-size studies is inconsistent

Correct treatment shows pi-excitation energy is not of order U

Abstract

Greiter claimed erroneously that the pi-excitation of the Hubbard model has an energy of the order of U. This mistake originates from a inconsistent treatment of the two particle Hartree energy and the Hartee correction to the chemical potential. In any self-consistent calculations, these two contributions cancel exactly, as shown by Kohn, Luttinger and Ward. We also show that his interpretation of the finite-size studies is inconsistent.