The Green's Function of the Holstein Polaron

Abstract

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.

21 pages, 54 figures

References in corpus (6)

• Green's function of a dressed particle
• Orbital ordering phenomena in $d$- and $f$-electron systems
• Quantum Monte Carlo and variational approaches to the Holstein model
• Photoemission spectra of many-polaron systems
• Spectral Properties of Holstein and Breathing Polarons
• Holstein polaron in two and three dimensions by quantum Monte Carlo

Cited by in corpus (7)

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• Phase diagram of the Holstein polaron in one dimension
• Survival of the Dirac points in rippled graphene
• Holstein polaron: the effect of multiple phonon modes
• Neutral triplet Collective Mode as a new decay channel in Graphite