The Green's Function of the Holstein Polaron

TL;DR

This paper introduces a new analytical approximation for the Green's function of a Holstein polaron that is both highly accurate and computationally efficient, valid across various parameters and satisfying key spectral sum rules.

Contribution

The authors develop a novel approximation method by summing self-energy diagrams with momentum averaging, improving accuracy over existing models for the Holstein polaron Green's function.

Findings

Exact in zero bandwidth and zero electron-phonon coupling limits

Satisfies the first six spectral sum rules exactly

Accurately matches numerical data across parameter space

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.