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arXiv:cond-mat/0610482

Comment on ``Orbital-selective Mott transitions in two-band Hubbard models''

A. Liebsch

Published Oct 17, 2006• 0 citations
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Abstract

A recent paper by Bluemer et al. [cond-mat/0609758] again criticizes earlier QMC/DMFT results by Liebsch [Phys. Rev. B {\bf 70}, 165103 (2004)]. This criticism is shown to be unfounded.
DOI
10.48550/arxiv.cond-mat/0610482

Related papers

Comment on: "Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures" by C. Knecht, N. Bluemer, and P. G. J. van Dongen, cond-mat/0505106

A. Liebsch

A detailed comparison of QMC/DMFT results for the non-isotropic two-band Hubbard model by Liebsch [Phys. Rev. B 70, 165103 (2004)] and C. Knecht, N. Bluemer, and P. G. J. van Dongen [cond-mat/0505106 (submitted to Phys. Rev. Lett.)] is given. Both results are shown to be in excellent agreement. Thus, the claims by Knecht et al.: ``The second transition [was] not seen in earlier studies using QMC and IPT'' and ``Our high-precision data correct earlier QMC results by Liebsch'' are shown to be unfounded.

arXiv:cond-mat/0506138•Jun 6, 2005•0 citations

Reply to "Comment on `Orbital-selective Mott transitions in the anisotropic two-band Hubbard model at finite temperatures'"

C. Knecht, Nils Blümer, P. G. J. van Dongen

In a Comment [cond-mat/0506138] on our recent e-print [cond-mat/0505106] Liebsch claimed "excellent correspondence" between our high-precision quantum Monte-Carlo (QMC) data for the anisotropic two-band Hubbard model with Ising type exchange couplings and his earlier QMC results. Liebsch also claimed that the sequence of two orbital-selective Mott transitions, identified by us in this model, had already been reported in his earlier work. Here we demonstrate that both claims are incorrect. We establish that Liebsch's previous QMC estimates for the quasiparticle weight Z have relative errors exceeding 100% near transitions and cannot be used to infer the existence of a second Mott transition (for U_{c2}~2.5). We further show that Liebsch's attribution of our findings to his own earlier work is disproved by the published record. Consequently, the Comment is unwarranted; all results and formulations of our e-print remain valid.

arXiv:cond-mat/0506450•Jun 17, 2005•0 citations

Orbital-selective Mott transitions in two-band Hubbard models

Nils Blümer, C. Knecht, Krunoslav Požgajčić +1 more

arXiv:cond-mat/0609758•Journal of Magnetism and Magnetic Materials•Nov 10, 2006•4 citations

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We reply to the comment (cond-mat/9806125) by Essler, Goehmann and Korepin, and show that their points are unfounded.

arXiv:cond-mat/9806225•Jun 18, 1998•0 citations

Numerical and analytical approaches to strongly correlated electron systems

C. Knecht

In this thesis we consider three different models for strongly correlated electrons, namely a multi-band Hubbard model as well as the spinless Falicov-Kimball model, both with a semi-elliptical density of states in the limit of infinite dimensions d, and the attractive Hubbard model on a square lattice in d=2.\n\nIn the first part, we study a two-band Hubbard model with unequal bandwidths and anisotropic Hund's rule coupling (J_z-model) in the limit of infinite dimensions within the dynamical mean-field theory (DMFT). Here, the DMFT impurity problem is solved with the use of quantum Monte Carlo (QMC) simulations. Our main result is that the J_z-model describes the occurrence of an orbital-selective Mott transition (OSMT), in contrast to earlier findings. We investigate the model with a high-precision DMFT \nalgorithm, which was developed as part of this thesis and which supplements QMC with a high-frequency expansion of the self-energy.\nThe main advantage of this scheme is the extraordinary accuracy of the numerical solutions, which can be obtained already with moderate computational effort, so that studies of multi-orbital systems within the DMFT+QMC are strongly improved. We also found that a suitably defined\nFalicov-Kimball (FK) model exhibits an OSMT, revealing the close connection of the Falicov-Kimball physics to the J_z-model in the OSM phase.\n\nIn the second part of this thesis we study the attractive Hubbard model in two spatial dimensions within second-order self-consistent perturbation theory.\nThis model is considered on a square lattice at finite doping and at low temperatures. Our main result is that the predictions of first-order perturbation theory (Hartree-Fock approximation) are renormalized by a factor of the order of unity even at arbitrarily weak interaction (U->0). The \nrenormalization factor q can be evaluated as a function of the filling n for 0<n<1. In the limit n->0, the q-factor vanishes, signaling the divergence of self-consistent perturbation theory in this limit. Thus we present the first asymptotically exact results at weak-coupling for the negative-U Hubbard model in d=2 at finite doping.

•Jan 1, 2006•1 citation

Orbital-selective Mott transitions in the degenerate Hubbard model

昌久 古賀, Akihisa Koga

•Jan 1, 2004•0 citations
A detailed comparison of QMC/DMFT results for the non-isotropic two-band Hubbard model by Liebsch [Phys. Rev. B 70, 165103 (2004)] and C. Knecht, N. Bluemer, and P. G. J. van Dongen [cond-mat/0505106 (submitted to Phys. Rev. Lett.)] is given. Both results are shown to be in excellent agreement. Thus, the claims by Knecht et al.: ``The second transition [was] not seen in earlier studies using QMC and IPT'' and ``Our high-precision data correct earlier QMC results by Liebsch'' are shown to be unfounded.
In a Comment [cond-mat/0506138] on our recent e-print [cond-mat/0505106] Liebsch claimed "excellent correspondence" between our high-precision quantum Monte-Carlo (QMC) data for the anisotropic two-band Hubbard model with Ising type exchange couplings and his earlier QMC results. Liebsch also claimed that the sequence of two orbital-selective Mott transitions, identified by us in this model, had already been reported in his earlier work. Here we demonstrate that both claims are incorrect. We establish that Liebsch's previous QMC estimates for the quasiparticle weight Z have relative errors exceeding 100% near transitions and cannot be used to infer the existence of a second Mott transition (for U_{c2}~2.5). We further show that Liebsch's attribution of our findings to his own earlier work is disproved by the published record. Consequently, the Comment is unwarranted; all results and formulations of our e-print remain valid.
In this thesis we consider three different models for strongly correlated electrons, namely a multi-band Hubbard model as well as the spinless Falicov-Kimball model, both with a semi-elliptical density of states in the limit of infinite dimensions d, and the attractive Hubbard model on a square lattice in d=2.\n\nIn the first part, we study a two-band Hubbard model with unequal bandwidths and anisotropic Hund's rule coupling (J_z-model) in the limit of infinite dimensions within the dynamical mean-field theory (DMFT). Here, the DMFT impurity problem is solved with the use of quantum Monte Carlo (QMC) simulations. Our main result is that the J_z-model describes the occurrence of an orbital-selective Mott transition (OSMT), in contrast to earlier findings. We investigate the model with a high-precision DMFT \nalgorithm, which was developed as part of this thesis and which supplements QMC with a high-frequency expansion of the self-energy.\nThe main advantage of this scheme is the extraordinary accuracy of the numerical solutions, which can be obtained already with moderate computational effort, so that studies of multi-orbital systems within the DMFT+QMC are strongly improved. We also found that a suitably defined\nFalicov-Kimball (FK) model exhibits an OSMT, revealing the close connection of the Falicov-Kimball physics to the J_z-model in the OSM phase.\n\nIn the second part of this thesis we study the attractive Hubbard model in two spatial dimensions within second-order self-consistent perturbation theory.\nThis model is considered on a square lattice at finite doping and at low temperatures. Our main result is that the predictions of first-order perturbation theory (Hartree-Fock approximation) are renormalized by a factor of the order of unity even at arbitrarily weak interaction (U->0). The \nrenormalization factor q can be evaluated as a function of the filling n for 0<n<1. In the limit n->0, the q-factor vanishes, signaling the divergence of self-consistent perturbation theory in this limit. Thus we present the first asymptotically exact results at weak-coupling for the negative-U Hubbard model in d=2 at finite doping.