Electron correlations in one dimension: The Hubbard model

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Abstract
Applicability of the Hubbard model (HM) to one-dimensional solids is investigated by careful analysis of the introduced approximations and by analytical calculation of the integrals. Consistency with the other approximations implies the neglect of interbond-charge-repulsion integrals. If the interelectronic potential is long range, the extended HM is adequate. On the contrary, for highly screened potentials intersite charge repulsion terms loose their importance in favor of the bond-site terms. The extended HM is then replaced by a new model, which in the mean-field treatment reduces to the simple HM.

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