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arXiv:cond-mat/0509443

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

M. Feldbacher, Ryotaro Arita, Karsten Held, Fakher F. Assaad

Published Sep 16, 2005• 0 citations

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.

DOI: 10.48550/arxiv.cond-mat/0509443

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Feldbacher, Held, and Assad Reply:

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In our reply, we show that the objections put forward in cond-mat/0508763 concerning our paper, Phys. Rev. Lett. 93, 136405 (2004), are not valid: (i) There is no orthogonality catastrophe (OC) for our calculations, and it is also generally not ``unpractical'' to avoid it. (ii) The OC does not affect our results.

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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.

We develop a projective quantum Monte Carlo algorithm of the Hirsch-Fye type for obtaining ground state properties of the Anderson impurity model. This method is employed to solve the self-consistency equations of dynamical mean field theory. It is shown that the approach converges rapidly to the ground state so that reliable zero-temperature results are obtained. As a first application, we study the Mott-Hubbard metal-insulator transition of the frustrated one-band Hubbard model, reconfirming the numerical renormalization group results.

In a recent Letter, Kuroki and Aoki [Phys. Rev. Lett. 76, 440 (1996)] presented quantum Monte-Carlo (QMC) results for pairing correlations in the three-band Hubbard model, which describes the Cu-d_{x^2-y^2} and O-p_{x,y} orbitals present in the CuO_2 planes of high-T_c materials. In this comment we argue that (i) the used parameter set is not appropriate for the description of high-T_c materials since it does not satisfy the minimal requirement of a charge-transfer gap at half-filling, and (ii) the observed increase in the d_{x^2-y^2} channel is dominantly produced by the pair-field correlations without the vertex part. Hence, the claim of evidence of ODLRO is not justified.

On the basis of an analysis of the numerical results corresponding to the half-filled 1D t-t'-V model on some finite lattices, Kokalj and Prelovsek (KP) have in a recent paper [Phys. Rev. B 78, 153103 (2008), arXiv:arXiv:0803.4468] concluded that the Luttinger theorem (LT) does not apply for the Mott-Hubbard (MH) insulating phase of this model (i.e. for V >> t) in the thermodynamic limit; KP even suggested, incorrectly, that failure of the LT were apparent for a half-filled finite system consisting of N=26 lattice sites. By employing a simple model for the self-energy Sigma of a MH state, we show that the finite-size-scaling approach of the type utilised by KP is not reliable for the system sizes considered by KP. On the basis of the equivalence of the model under consideration (at half-filling and for t'/t << 1) and the XXZ spin-chain Hamiltonian for SU(2) spins, we further show that for V > V_c(t,t') the system under consideration has a charge-density-wave (CDW) ground state (GS) in the thermodynamic limit, corresponding to a doubling of the unit cell in comparison with that specific to the underlying lattice. Although this GS is also insulating, its spectral gap is due to the broken translational symmetry of the GS; it is not a correlation-induced MH gap. The LT is therefore a priori valid for this GS. This fact establishes that the conclusion by KP is indeed erroneous. Finally, we present a heuristic argument due to Volovik that sheds light on the mechanism underlying the robustness of the LT. In an appendix, we present the details of the calculation of the single-particle Green function of the broken-symmetry GS of the model under consideration by means of bosonization and in terms of the form factors of a class of soliton-generating fields pertaining to the quantum sine-Gordon Hamiltonian. [Shortened abstract]