The Green's Function of the Holstein Polaron

Details The Green's Function of the Holstein Polaron The Green's Function of the Holstein Polaron

2006-09-22

arxiv.org/abs/cond-mat/0609597v1

Phys. Rev. B 74, 245104 (2006)

Physics

Condensed Matter

Strongly Correlated Electrons

21 pages, 54 figures

Scientific paper

10.1103/PhysRevB.74.245104

We present a novel, 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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