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Reviews of topical problems


Hubbard model of strong correlations


Mikheev Institute of Metal Physics, Ural Division of the Russian Academy of Sciences, S Kovalevskoi str. 18, Ekaterinburg, 620108, Russian Federation

A state-of-the-art review is given of the investigations of the Hubbard model, which is the main model used in the theory of strongly correlated electron systems. It is shown how the main correlation effects — the metal-insulator phase transition, the appearance of localised magnetic moments, and the breakdown of the Fermi-liquid behaviour — appear in the case of strong electron correlations when U ~ W, where U is the Coulomb repulsion parameter and W is the band width. Different approaches to the problem, not based on perturbation theory in terms of the parameter U/W or W/U, are presented. A new method in the theory of strongly correlated systems, in which the limit of infinite number of dimensions of space, d = infty, is the main feature of the review. The physical results obtained by this approach are compared with those deduced by traditional methods. An overview of the behaviour of strongly correlated systems is given for wide ranges of the model parameters U and W, and of the electron density n.

Fulltext pdf (660 KB)
Fulltext is also available at DOI: 10.1070/PU1995v038n04ABEH000081
PACS: 71.27.+a
DOI: 10.1070/PU1995v038n04ABEH000081
URL: https://ufn.ru/en/articles/1995/4/b/
A1995RH54700002
Citation: Izyumov Yu A "Hubbard model of strong correlations" Phys. Usp. 38 385–408 (1995)
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Îðèãèíàë: Èçþìîâ Þ À «Ìîäåëü Õàááàðäà â ðåæèìå ñèëüíûõ êîððåëÿöèé» ÓÔÍ 165 403–427 (1995); DOI: 10.3367/UFNr.0165.199504b.0403

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