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Homogeneity in the Ground State of the Two-Dimensional Falicov-Kimball Model

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On Three Levels

Part of the book series: NATO ASI Series ((NSSB,volume 324))

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Abstract

The Falicov-Kimball model is one of the simplest models of itinerant fermions with an on site interaction. It consists of spinless fermions on a lattice which may hop between nearest neighbor sites and which interact with another species of particles which are not allowed to hop. There are several physical interpretations of this model. We will use the interpretation in which one thinks of the hopping fermions as electrons and the static particles as nuclei. The Hamiltonian is

$$ H = \sum\limits_{{x,y:|x - y| = 1}} {c_{x}^{ + }} {{c}_{y}} - U\sum\limits_{x} {c_{x}^{ + }} {{c}_{x}}W(x) $$

where c † x and c x are creation and annihilation operators for the electrons, W(x) = 1 if there is a nuclei at x and W(x) = 0 if there is not.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA

    T. Kennedy

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  1. T. Kennedy
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Editors and Affiliations

  1. Katholieke Universiteit Leuven, Leuven, Belgium

    André Verbeure

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© 1994 Springer Science+Business Media New York

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Kennedy, T. (1994). Homogeneity in the Ground State of the Two-Dimensional Falicov-Kimball Model. In: Fannes, M., Maes, C., Verbeure, A. (eds) On Three Levels. NATO ASI Series, vol 324. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2460-1_4

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  • DOI: https://doi.org/10.1007/978-1-4615-2460-1_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6047-6

  • Online ISBN: 978-1-4615-2460-1

  • eBook Packages: Springer Book Archive

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