The Hubbard Model

Its Physics and Mathematical Physics

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

Part of the NATO ASI Series book series (NSSB, volume 343)

Table of contents

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

    1. Holger Frahm, Andreas Schadschneider
      Pages 21-28
    2. D. Foerster, N. Schopohl
      Pages 63-69
    3. Vladimir E. Korepin, Fabian H. L. Eßler
      Pages 71-80
    4. Fabian H. L. Eßler, Vladimir E. Korepin
      Pages 81-88
    5. Christian Kübert, Alejandro Muramatsu
      Pages 103-111
    6. J. Pérez-Conde, P. Pfeuty
      Pages 113-116
    7. J. M. P. Carmelo, A. H. Castro-Neto, D. K. Campbell
      Pages 117-124
  3. Infinite in All Directions: Large Coupling, High Dimensions, and Many Components

    1. Gabriel Kotliar, Marcelo J. Rosenberg
      Pages 155-166
    2. V. Janiš, M. Ulmke, D. Vollhardt
      Pages 167-174
    3. V. Ya. Krivnov, A. A. Ovchinnikov, V. O. Cheranovskii
      Pages 175-184
    4. P. G. J. van Dongen
      Pages 185-192
    5. Peter Horsch, Walter Stephan
      Pages 193-200
    6. M. Di Stasio, G. Morandi, A. Tagliacozzo
      Pages 201-208
    7. E. Arrigoni, C. Castellani, R. Raimondi, G. C. Strinati
      Pages 209-216
  4. Fermi Liquid versus Luttinger Liquid

  5. Perturbative, Mean Field, Variational, and Numerical Studies

    1. F. Guinea, E. Louis, J. A. Vergés
      Pages 295-302
    2. J. Galán, J. A. Vergés
      Pages 303-306
    3. H. Q. Lin, E. R. Gagliano, D. K. Campbell, E. H. Fradkin, J. E. Gubernatis
      Pages 315-326
    4. R. Preuss, F. F. Assaad, A. Muramatsu, W. Hanke
      Pages 331-340
    5. J. A. Vergés, F. Guinea, J. Galán, G. Chiappe, E. Louis
      Pages 341-348
    6. E. Louis, G. Chiappe, J. Galán, F. Guinea, J. A. Vergés
      Pages 349-356
  6. Experiments and Physical Applications

  7. Back Matter
    Pages 401-407

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).


electron mathematical physics scattering

Editors and affiliations

  • Dionys Baeriswyl
    • 1
  • David K. Campbell
    • 2
  • Jose M. P. Carmelo
    • 3
  • Francisco Guinea
    • 3
  • Enrique Louis
    • 4
  1. 1.University of FribourgFribourgSwitzerland
  2. 2.University of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.University of MadridMadridSpain
  4. 4.University of AlicanteAlicanteSpain

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag US 1995
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4899-1044-8
  • Online ISBN 978-1-4899-1042-4
  • Series Print ISSN 0258-1221
  • Buy this book on publisher's site
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