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Physical review. B, Condensed matter

Ground-state energy of the half-filled one-dimensional Hubbard model

Eleftherios N. Economou, P. Poulopoulos

Published Dec 1, 1979• 24 citations
Publisher

Abstract

The exact result of Lieb and Wu is recast as an asymptotic series in the small-U limit. This series permits comparisons with a recent approximate method and with the perturbation expansion.Received 25 July 1979DOI:https://doi.org/10.1103/PhysRevB.20.4756©1979 American Physical Society

DOI
10.1103/physrevb.20.4756

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The exact result of Lieb and Wu is recast as an asymptotic series in the small-U limit. This series permits comparisons with a recent approximate method and with the perturbation expansion.Received 25 July 1979DOI:https://doi.org/10.1103/PhysRevB.20.4756©1979 American Physical Society
We investigate the ground state of the Hubbard model in one and two dimensions. Long perturbation expansions in t/U, i.e., about the atomic limit, are computed for the ground-state energy of finite lattices with N\ensuremath{\le}10 for arbitrary electron density. We also extend the series for the one-dimensional infinite lattice by expanding the Bethe-ansatz equations. Pad\'e-approximant analysis of the series shows a distribution of singularities that varies dramatically with the electron density n. We also investigate the effect of inclusion of next-nearest-neighbor hopping. This appears to have little effect at half-filling but is significant away from half-filling.