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The Hubbard model: Some Rigorous Results and Open Problems

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Book cover Condensed Matter Physics and Exactly Soluble Models

Abstract

The Hubbard model of interacting electrons, like the Ising model of spin-spin interactions, is the simplest possible model displaying many “real world” features, but it is much more difficult to analyze qualitatively than the Ising model. After a third of a century of research, we are still not sure about many of its basic properties. This mini-review will explore what is known rigorously about the model and it will attempt to describe some open problems that are possibly within the range of rigorous mathematical analysis.

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Authors and Affiliations

  1. Departments of Mathematics and Physics, Princeton University, Princeton, NJ, 08544, USA

    Elliott H. Lieb

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  1. Elliott H. Lieb
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Editors and Affiliations

  1. Department of Mathematics, University of California, One Shields Ave., 95616-8633, Davis, CA, USA

    Bruno Nachtergaele

  2. Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Jan Philip Solovej

  3. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090, Wien, Austria

    Jakob Yngvason

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Lieb, E.H. (2004). The Hubbard model: Some Rigorous Results and Open Problems. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Condensed Matter Physics and Exactly Soluble Models. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06390-3_4

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  • DOI: https://doi.org/10.1007/978-3-662-06390-3_4

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  • Print ISBN: 978-3-642-06093-9

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