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Physics Letters A

Intermediate coupling theory for the multidimensional polaron

Shreekantha Sil, Ashok Chatterjee

Published Sep 1, 1989• 10 citations
Publisher
DOI
10.1016/0375-9601(89)90549-5

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A general method is presented for obtaining an accurate intermediate-coupling theory from weak- and strong-coupling perturbation theory. The method uses two-point Pad\'e approximants to extrapolate (low-order) expansions about the weak- and the strong-coupling limits into the intermediate-coupling regime. The method is used to evaluate the ground-state energy and effective mass of the polaron with gratifying success. In addition, the weak-coupling perturbation theory of the polaron dispersion relation, ground-state energy, and effective mass are extended to fourth, sixth, and fourth order, respectively. A scheme based on two-point Pad\'e approximants is used to obtain an optimal polaron dispersion relation.
The single-polaron band structure of the Holstein model in one and two dimensions is studied using a new form of resummed strong-coupling perturbation theory. Well converged results are obtained for phonon frequencies of the order of the hopping integral and strong to intermediate electron-phonon coupling. The polaron band structure at intermediate coupling is shown to deviate markedly from that of a nearest-neighbor tight-binding model, and is in fact similar in shape to the prediction of weak-coupling self-consistent perturbation theory.