Green's function of a dressed particle

TL;DR

This paper introduces a novel approximation method for calculating Green's functions of dressed particles, accurately satisfying spectral sum rules by averaging over free propagator momenta, applicable to models like the Holstein polaron.

Contribution

It proposes a new approximation technique that sums all diagrams with averaged free propagator momenta, improving accuracy over traditional methods like SCBA.

Findings

Satisfies the first six spectral weight sum rules exactly

Achieves high accuracy for higher sum rules, especially at extreme coupling strengths

Applicable to models beyond the Holstein polaron

Abstract

We present a new, highly efficient yet accurate approximation for the Green's functions of dressed particles, using the Holstein polaron as an example. Instead of summing a subclass of diagrams (e.g. the non-crossed ones, in the self-consistent Born approximation (SCBA)), we sum all the diagrams, but with each diagram averaged over its free propagators' momenta. 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. Possible generalizations to other models are also discussed.