Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9401023 · Physical review. B, Condensed matter

Asymptotic solution of the infinite-dimensional Hubbard model

X. Y. Zhang, G. M. Zhang

Published Mar 15, 1994• 1 citation
arXivHTMLPDF

Abstract

We present an asymptotically exact solution of the infinite-dimensional Hubbard model at a special interaction strength ${\mathit{U}}_{\mathit{T}}$ corresponding to the strong-coupling Fermi-liquid fixed point. This solution is intimately related to the Toulouse limit of the single-impurity Kondo model and the symmetric Anderson model in its strong-coupling limit.

DOI
10.1103/physrevb.49.7929

Related papers

Hubbard model in infinite dimensions

Antoine Georges, Gabriel Kotliar

We present an exact mapping of the Hubbard model in infinite dimensions onto a single-impurity Anderson (or Wolff) model supplemented by a self-consistency condition. This provides a mean-field picture of strongly corrrelated systems, which becomes exact as d\ensuremath{\rightarrow}\ensuremath{\infty}. We point out a special integrable case of the mean-field equations, and study the general case using a perturbative renormalization group around the atomic limit. Three distinct Fermi-liquid regimes arise, corresponding to the Kondo, mixed-valence, and empty-orbitals regimes of the single-impurity problem. The Kondo resonance and the satellite peaks of the single-impurity model correspond to the quasiparticle and Hubbard-bands features of the Hubbard model, respectively.

Physical review. B, Condensed matter•Mar 15, 1992•1,073 citations

Metallic non-Fermi-liquid phases of an extended Hubbard model in infinite dimensions

Qimiao Si A, Gabriel Kotliar

We study an extended Hubbard model in the limit of infinite dimensions and its zero-dimensional counterpart, a generalized asymmetric Anderson model. In the impurity model we find three kinds of mixed valence states: (a) the usual strong-coupling state in which a resonance forms at the Fermi level; (b) a weak-coupling state in which neither the impurity spin nor the impurity charge degrees of freedom are quenched; and (c) an intermediate-coupling state where the spin but not the charge degree of freedom is quenched. The corresponding phases of the extended Hubbard model in infinite dimensions are (a) a Fermi liquid; (b) a non-Fermi-liquid state with incoherent charge and spin excitations; and (c) a non-Fermi-liquid state with incoherent charge but coherent spin excitations. The non-Fermi-liquid phases are incoherent metallic states with vanishing quasiparticle residue, self-similar local correlation functions, and asymptotically decoupled charge and spin excitations. The non-Fermi-liquid phases occur for a wide range of parameters.

arXiv:cond-mat/9307060•Physical review. B, Condensed matter•Nov 1, 1993•41 citations

A SELF-ENERGY FUNCTIONAL FOR THE INFINITE-DIMENSIONAL HUBBARD MODEL

Y.M. Li, N. d’Ambrumenil

We present an approximate self-energy functional for the infinite-dimensional Hubbard model. This functional is a natural extension of the exact solution of the Falicov-Kimball model to the spin-symmetric case, and is exact in the uncorrelated and atomic limits. Using the functional we calculate the susceptibility and the specific heat for the Lorentzian density of states. We find that the susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations to a Fermi liquid state at low temperature via a Kondo-type anomaly. The specific heat shows a peak at the corresponding Kondo temperature.

Modern Physics Letters B•Dec 10, 1992•7 citations

Solution of the Two-Impurity, Two-Channel Kondo Model

Antoine Georges, Anirvan M. Sengupta

We solve the two-impurity, two-channel Kondo model using a combination of conformal invariance and bosonization techniques. In the odd-even symmetric case, the RKKY interaction is exactly marginal, resulting in a line of non-Fermi-liquid fixed points. Explicit formulas are given for the critical exponents and for the finite-size spectrum, which depend continuously on a single parameter. The marginal line spans a range of values of the RKKY coupling $I$ which goes from the infinitely strong ferromagnetic point $I\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}+\ensuremath{\infty}$ to a finite antiferromagnetic critical value ${I}_{\mathrm{min}}<0$ beyond which a Fermi liquid is recovered. When the odd-even symmetry is broken, the marginal line is unstable for ferromagnetic $I$, while for antiferromagnetic $I$ it extends into a manifold of fixed points.

arXiv:cond-mat/9405054•Physical Review Letters•Apr 3, 1995•33 citations

Strongly Correlated Systems in Infinite Dimensions and Their Zero Dimensional Counterparts

Antoine Georges, Gabriel Kotliar, Qimiao Si A

We extend a mapping from infinite dimensional to zero dimensional (impurity) models to derive mean field equations of several strongly correlated systems which become exact in infinite dimensions. We discuss various magnetic phases of the Hubbard model, the periodic Anderson model the Kondo lattice and the Falicov Kimball model and we relate them to different impurity models. Qualitative insights into these models is gained from the exact results obtained for their zero dimensional counterparts.

International Journal of Modern Physics B•Mar 1, 1992•67 citations

Asymptotically exact solution of the multichannel resonant-level model

Guang-Ming Zhang, Zhao-Bin Su, Lu Yu

An asymptotically exact partition function of the multichannel resonant-level model is obtained through Tomonaga-Luttinger bosonization. A Fermi-liquid vs non-Fermi-liquid transition, resulting from a competition between the Kondo resonance and the x-ray edge singularity, is elucidated explicitly via renormalization-group theory. In the strong-coupling limit, the model is renormalized to the Toulouse limit.

arXiv:cond-mat/9401059•Physical review. B, Condensed matter•Mar 15, 1994•9 citations
We present an asymptotically exact solution of the infinite-dimensional Hubbard model at a special interaction strength UT{\mathit{U}}_{\mathit{T}}UT​ corresponding to the strong-coupling Fermi-liquid fixed point. This solution is intimately related to the Toulouse limit of the single-impurity Kondo model and the symmetric Anderson model in its strong-coupling limit.
We present an exact mapping of the Hubbard model in infinite dimensions onto a single-impurity Anderson (or Wolff) model supplemented by a self-consistency condition. This provides a mean-field picture of strongly corrrelated systems, which becomes exact as d\ensuremath{\rightarrow}\ensuremath{\infty}. We point out a special integrable case of the mean-field equations, and study the general case using a perturbative renormalization group around the atomic limit. Three distinct Fermi-liquid regimes arise, corresponding to the Kondo, mixed-valence, and empty-orbitals regimes of the single-impurity problem. The Kondo resonance and the satellite peaks of the single-impurity model correspond to the quasiparticle and Hubbard-bands features of the Hubbard model, respectively.
We study an extended Hubbard model in the limit of infinite dimensions and its zero-dimensional counterpart, a generalized asymmetric Anderson model. In the impurity model we find three kinds of mixed valence states: (a) the usual strong-coupling state in which a resonance forms at the Fermi level; (b) a weak-coupling state in which neither the impurity spin nor the impurity charge degrees of freedom are quenched; and (c) an intermediate-coupling state where the spin but not the charge degree of freedom is quenched. The corresponding phases of the extended Hubbard model in infinite dimensions are (a) a Fermi liquid; (b) a non-Fermi-liquid state with incoherent charge and spin excitations; and (c) a non-Fermi-liquid state with incoherent charge but coherent spin excitations. The non-Fermi-liquid phases are incoherent metallic states with vanishing quasiparticle residue, self-similar local correlation functions, and asymptotically decoupled charge and spin excitations. The non-Fermi-liquid phases occur for a wide range of parameters.
We present an approximate self-energy functional for the infinite-dimensional Hubbard model. This functional is a natural extension of the exact solution of the Falicov-Kimball model to the spin-symmetric case, and is exact in the uncorrelated and atomic limits. Using the functional we calculate the susceptibility and the specific heat for the Lorentzian density of states. We find that the susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations to a Fermi liquid state at low temperature via a Kondo-type anomaly. The specific heat shows a peak at the corresponding Kondo temperature.
We solve the two-impurity, two-channel Kondo model using a combination of conformal invariance and bosonization techniques. In the odd-even symmetric case, the RKKY interaction is exactly marginal, resulting in a line of non-Fermi-liquid fixed points. Explicit formulas are given for the critical exponents and for the finite-size spectrum, which depend continuously on a single parameter. The marginal line spans a range of values of the RKKY coupling III which goes from the infinitely strong ferromagnetic point $I\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}+\ensuremath{\infty}$ to a finite antiferromagnetic critical value Imin<0{I}_{\mathrm{min}}<0Imin​<0 beyond which a Fermi liquid is recovered. When the odd-even symmetry is broken, the marginal line is unstable for ferromagnetic III, while for antiferromagnetic III it extends into a manifold of fixed points.