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The Hubbard Model

Its Physics and Mathematical Physics

  • Book
  • © 1995

Overview

Editors:
  1. Dionys Baeriswyl

    1. University of Fribourg, Fribourg, Switzerland

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  2. David K. Campbell

    1. University of Illinois at Urbana-Champaign, Urbana, USA

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  3. Jose M. P. Carmelo

    1. University of Madrid, Madrid, Spain

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  4. Francisco Guinea

    1. University of Madrid, Madrid, Spain

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  5. Enrique Louis

    1. University of Alicante, Alicante, Spain

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Part of the book series: NATO Science Series B: (NSSB, volume 343)

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Table of contents (44 chapters)

  1. Front Matter

    Pages i-xii
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  2. Solvable Models, Rigorous Results, and Advances in Formalism

    1. The Hubbard Model: Some Rigorous Results and Open Problems

      • Elliott H. Lieb
      Pages 1-19

    2. On the Bethe Ansatz Soluble Degenerate Hubbard Model

      • Holger Frahm, Andreas Schadschneider
      Pages 21-28

    3. Thermodynamical Properties of the Exactly Solvable 1/r-Hubbard- and 1/r-tJ-Model

      • Florian Gebhard
      Pages 29-38

    4. Hierarchy of 1D Electron Models with Long-Range Interaction

      • Norio Kawakami
      Pages 39-46

    5. One-Dimensional Luttinger Liquid of Particles for a Class of Infinitely Repulsive Interactions: Exact Solution

      • G. Gómez-Santos
      Pages 47-54

    6. Exact Results for Spin and Charge Dynamics of Electrons with Supersymmetry

      • Y. Kuramoto
      Pages 55-62

    7. Hidden Symmetry of Strongly Correlated Fermons

      • D. Foerster, N. Schopohl
      Pages 63-69

    8. Symmetries of Strongly Correlated Electrons

      • Vladimir E. Korepin, Fabian H. L. Eßler
      Pages 71-80

    9. Exact Results on a Supersymmetric Extended Hubbard Model

      • Fabian H. L. Eßler, Vladimir E. Korepin
      Pages 81-88

    10. Functional Integrals for Correlated Electrons

      • H. J. Schulz
      Pages 89-102

    11. Charge-Spin Separation and Pairing in a Generalized Hubbard Model

      • Christian Kübert, Alejandro Muramatsu
      Pages 103-111

    12. A Renormalization Procedure for the Hubbard Model

      • J. Pérez-Conde, P. Pfeuty
      Pages 113-116

    13. New Operator Algebra for the Hubbard Chain

      • J. M. P. Carmelo, A. H. Castro-Neto, D. K. Campbell
      Pages 117-124

    14. Exact Results and Conjectures on the Adiabatic Holstein-Hubbard Model at Large Electron-Phonon Coupling

      • Serge Aubry
      Pages 125-143

    15. Ferromagnetism in Correlated Electron Systems: A New Class of Rigorous Criteria

      • Rainer Strack, Dieter Vollhardt
      Pages 145-153

  3. Infinite in All Directions: Large Coupling, High Dimensions, and Many Components

    1. The Mott Transition in Infinite Dimensions: Old Ideas and Some Surprises

      • Gabriel Kotliar, Marcelo J. Rosenberg
      Pages 155-166

    2. The Hubbard Model with Local Disorder in d = ∞

      • V. JaniÅ¡, M. Ulmke, D. Vollhardt
      Pages 167-174

    3. The Hubbard Model with Infinite Interaction: Magnetic Properties

      • V. Ya. Krivnov, A. A. Ovchinnikov, V. O. Cheranovskii
      Pages 175-184

    4. The Extended Hubbard Model at Large Interaction

      • P. G. J. van Dongen
      Pages 185-192
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Keywords

About this book

In the slightly more than thirty years since its formulation, the Hubbard model has become a central component of modern many-body physics. It provides a paradigm for strongly correlated, interacting electronic systems and offers insights not only into the general underlying mathematical structure of many-body systems but also into the experimental behavior of many novel electronic materials. In condensed matter physics, the Hubbard model represents the simplest theoret­ ical framework for describing interacting electrons in a crystal lattice. Containing only two explicit parameters - the ratio ("Ujt") between the Coulomb repulsion and the kinetic energy of the electrons, and the filling (p) of the available electronic band - and one implicit parameter - the structure of the underlying lattice - it appears nonetheless capable of capturing behavior ranging from metallic to insulating and from magnetism to superconductivity. Introduced originally as a model of magnetism of transition met­ als, the Hubbard model has seen a spectacular recent renaissance in connection with possible applications to high-Tc superconductivity, for which particular emphasis has been placed on the phase diagram of the two-dimensional variant of the model. In mathematical physics, the Hubbard model has also had an essential role. The solution by Lieb and Wu of the one-dimensional Hubbard model by Bethe Ansatz provided the stimulus for a broad and continuing effort to study "solvable" many-body models. In higher dimensions, there have been important but isolated exact results (e. g. , N agoaka's Theorem).

Editors and Affiliations

  • University of Fribourg, Fribourg, Switzerland

    Dionys Baeriswyl

  • University of Illinois at Urbana-Champaign, Urbana, USA

    David K. Campbell

  • University of Madrid, Madrid, Spain

    Jose M. P. Carmelo, Francisco Guinea

  • University of Alicante, Alicante, Spain

    Enrique Louis

Bibliographic Information

  • Book Title: The Hubbard Model

  • Book Subtitle: Its Physics and Mathematical Physics

  • Editors: Dionys Baeriswyl, David K. Campbell, Jose M. P. Carmelo, Francisco Guinea, Enrique Louis

  • Series Title: NATO Science Series B:

  • DOI: https://doi.org/10.1007/978-1-4899-1042-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1995

  • Hardcover ISBN: 978-0-306-45003-7Published: 30 November 1995

  • Softcover ISBN: 978-1-4899-1044-8Published: 19 June 2013

  • eBook ISBN: 978-1-4899-1042-4Published: 11 November 2013

  • Series ISSN: 0258-1221

  • Edition Number: 1

  • Number of Pages: XII, 407

  • Topics: Nuclear Physics, Heavy Ions, Hadrons, Theoretical, Mathematical and Computational Physics

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