Green’s function of the Holstein polaron

Glen L. Goodvin, Mona Berciu, and George A. Sawatzky
Phys. Rev. B 74, 245104 – Published 5 December 2006

Abstract

We present a highly efficient yet accurate analytical approximation for the Green’s function of a Holstein polaron. It is obtained by summing all the self-energy diagrams, but with each self-energy diagram averaged over the momenta of its free propagators. The result becomes exact for both zero bandwidth and for zero electron-phonon coupling and is accurate everywhere in the parameter space. The resulting Green’s function satisfies exactly the first six spectral weight sum rules. All higher sum rules are satisfied with great accuracy, becoming asymptotically exact for coupling both much larger and much smaller than the free particle bandwidth. Comparison with existing numerical data also confirms this accuracy. We use this approximation to analyze in detail the redistribution of the spectral weight as the coupling strength varies.

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  • Received 21 September 2006

DOI:https://doi.org/10.1103/PhysRevB.74.245104

©2006 American Physical Society

Authors & Affiliations

Glen L. Goodvin, Mona Berciu, and George A. Sawatzky

  • Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1

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Issue

Vol. 74, Iss. 24 — 15 December 2006

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