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arXiv:cond-mat/0306438 · The European Physical Journal B

Fourth-order perturbation theory for the half-filled Hubbard model in infinite dimensions

S. Mahlert, F. Gebhard, E. Jeckelmann, R. M. Noack, Satoshi Nishimoto

Published Dec 1, 2003• 40 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2004-00005-5

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We use Brueckner–Goldstone perturbation theory to calculate the ground-state energy of the half-filled Hubbard model in infinite dimensions up to fourth order in the Hubbard interaction. We obtain the momentum distribution as a functional derivative of the ground-state energy with respect to the bare dispersion relation. The resulting expressions agree with those from Rayleigh–Schrödinger perturbation theory. Our results for the momentum distribution and the quasi-particle weight agree very well with those obtained earlier from Feynman–Dyson perturbation theory for the single-particle self-energy. We give the correct fourth-order coefficient in the ground-state energy which was not calculated accurately enough from Feynman–Dyson theory due to the insufficient accuracy of the data for the self-energy, and find a good agreement with recent estimates from quantum Monte Carlo calculations.
A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact quantum Monte Carlo results. The second-order iterated perturbation theory is shown to be quite accurate in calculating transition temperatures for retarded interactions, but is not as accurate for the self-energy or the irreducible vertex functions themselves. Iterated perturbation theory is carried out through fourth order for the Hubbard model. The self-energy is quite accurately reproduced by the theory, but the vertex functions are not. Anomalous behavior occurs near half-filling because the iterated perturbation theory is not a conserving approximation.