Abstract

The many-body Green functions for the three-dimensional electron–phonon Holstein model are calculated via the Feynman diagram technique. The lowest-order contributions to the one-electron self-energy are considered (the Hartree–Fock approximation). The chemical potential is adjusted to yield the desired band-filling. The temperature dependence of the chemical potential has the correct asymptotic form in the non-interacting limit. The behavior of the one-electron occupancy factor is examined for various parameter values of the model. Tian's theorem is satisfied at half-filling. Luttinger liquid behavior is observed in the strong electron–phonon coupling regime.

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