Some clarifications on cond-mat/0508763 by M. I. Katsnelson

TL;DR

This paper defends the validity of a projective quantum Monte Carlo method against criticisms, clarifying misconceptions about orthogonality catastrophe and emphasizing its practicality both at and off half-filling.

Contribution

The authors refute Katsnelson's claims by providing a detailed proof and clarification, reaffirming the method's validity and practicality in different electron filling scenarios.

Findings

Orthogonality catastrophe does not affect the method's validity.

The method is practical both at and off half-filling.

Katsnelson's objections are invalid based on the presented proofs.

Abstract

Katsnelson submitted his Comment on our paper "Projective Quantum Monte Carlo Method for the Anderson Impurity Model and its Application to Dynamical Mean Field Theory" to Phys. Rev. Lett. in May 2005. We proved in our report that this comment was incorrect since there is no orthogonality catastrophe for our calculation in Phys. Rev. Lett. 93, 136405 (2004) which is for half-filling. Now in cond-mat/0508763, Katsnelson incorporates our proof of the invalidity of his original Comment, based on Friedel's sum rule. Instead, he now claims that the projective quantum Monte Carlo method is "unpractical" off half-filling, overlooking that our calculations off half-filling (R. Arita and K. Held, LT24 conference proceedings and cond-mat/0508639) employ in practice a noninteracting trial Hamiltonian with the same electron density as the interacting Hamiltonian so that there is again no orthogonality catastrophe. Note added. In the revised version of his comment, Katsnelson gives proper credit to our proof. In our reply, we will present the original proof based on the Friedel sum rule. Moreover, we show that the orthogonality catastrophe does not affect our results. Katsnelson's objection is not valid.