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Strongly Correlated Magnetic and Superconducting Systems pp 1–32Cite as

An introduction to the Hubbard model

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Part of the book series: Lecture Notes in Physics ((LNP,volume 478))

Abstract

In these notes we review some of the basic features of the 2D Hubbard model, thought of as the appropriate model for the description of the Cu — O planes in the cuprate superconductors. We discuss breifly the weakcoupling regime of the model and, in the opposite limit, the mapping of the one band Hubbard model onto an AFM Heisenberg model at half filling and onto the t — J model below half filling. We discuss next Emery’s three band model and its mapping onto the so-called “spin-fermion” model. Its continuum limit is discussed by making use of an adiabatic followed by a gradient expansion. We review briefly how the model maps onto a nonlinear sigma model and some of the features of the latter.

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Author information

Authors and Affiliations

  1. Dipartimento di Fisica and INFM, Universita’ di Bologna, 46 Via Irnerio, I-40126, Bologna, Italy

    E. Ercolessi, G. Morandi & P. Pieri

  2. INFN, Universita’ di Bologna, Italy

    G. Morandi & P. Pieri

Authors
  1. E. Ercolessi
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  2. G. Morandi
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  3. P. Pieri
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Editor information

Germán Sierra Miguel A. Martín-Delgado

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© 1997 Springer-Verlag

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Ercolessi, E., Morandi, G., Pieri, P. (1997). An introduction to the Hubbard model. In: Sierra, G., Martín-Delgado, M.A. (eds) Strongly Correlated Magnetic and Superconducting Systems. Lecture Notes in Physics, vol 478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104632

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  • DOI: https://doi.org/10.1007/BFb0104632

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  • Print ISBN: 978-3-540-62476-9

  • Online ISBN: 978-3-540-49734-9

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