Systematic improvement of the Momentum Average approximation for the Green's function of a Holstein polaron

TL;DR

This paper enhances the Momentum Average approximation for the Holstein polaron's Green's function by systematically improving self-energy calculations, resulting in more accurate spectral features and better agreement with numerical data, especially in lower dimensions.

Contribution

The paper introduces a systematic method to improve the MA approximation for the Holstein polaron, maintaining computational efficiency while increasing accuracy.

Findings

Correctly locates polaron+phonon continuum

Achieves better quantitative agreement with numerical data

Finds larger corrections in lower-dimensional systems

Abstract

We show how to systematically improve the Momentum Average (MA)approximation for the Green's function of a Holstein polaron, bysystematically improving the accuracy of the self-energy diagrams in such a way that they can still all be summed efficiently. This allows us to fix some of the problems of the MA approximation, e.g. we now find the expected polaron+phonon continuum at the correct location, and a momentum-dependent self-energy. The quantitative agreement with numerical data is further improved, as expected since the number of exactly satisfied spectral weight sum rules is increased. The corrections are found to be larger in lower dimensional systems.