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Physics Letters A

Electron correlation in an extended Hubbard model

D.K. Ghosh

Published Aug 1, 1970• 8 citations
Publisher
DOI
10.1016/0375-9601(70)90038-1

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Using the local approach, we have performed a third·order perturbation calculation to investigate the effects of intra-atomic electron correlation and electron and spin correlation between nearest neighbour sites in the extended Hubbard model. We found that significant correction of the third order over the second order results and, in comparison with the results of the third-order perturbation where only the intra-atomic electron correlation is included, the influence of the electron and spin correlation between nearest neighbour sites on the correlation energy is non-negligible.
The Holstein-Hubbard model is studied in two dimensions to explore the nature of polarons as a function of hole concentration in the strong correlation regime. A series of canonical transformations is performed to obtain an effective extended Hubbard model which, in the strong on-site electron-electron correlation regime, transforms into a t-J model and is solved using the mean-field Hartree-Fock approximation (HFA). It is shown that the hopping parameter which is related to the bandwidth of the polaron is very small for low (x ≈ 0) and high (x ≈ 1) hole concentrations whereas the hopping parameter is much larger for the intermediate hole concentrations.
Currently, the extended Hubbard model, which is a good approximation only for narrow-band system, suggests that the width of polaron in polymer is heavily reduced by the electron-electron interaction. However, the polymers possess wide band, so the off-diagonal correlation cannot be neglected. We considered the effects of full electron-electron correlation on the width and the creation energy of polaron in polymer. In the case of strong screening, our results are greatly different from those of Hubbard model. This suggests that in polymer, the Hubbard model should be gone beyond.