Vertex-corrected perturbation theory for the electron-phonon problem with non-constant density of states

TL;DR

This paper develops vertex-corrected perturbation theories for the electron-phonon Holstein model, comparing their accuracy against quantum Monte Carlo results, especially in the infinite-dimensional limit.

Contribution

It introduces a series of weak-coupling perturbation theories with vertex corrections tailored for the Holstein model, aligning with known limits and benchmarking against numerical solutions.

Findings

Vertex corrections improve perturbation theory accuracy.

Comparison shows certain approximations closely match quantum Monte Carlo results.

The approach effectively captures electron-phonon interactions in the studied regime.

Abstract

A series of weak-coupling perturbation theories which include the lowest-order vertex corrections are applied to the attractive Holstein model in infinite dimensions. The approximations are chosen to reproduce the iterated perturbation theory in the limit of half-filling and large phonon frequency (where the Holstein model maps onto the Hubbard model). Comparison is made with quantum Monte Carlo solutions to test the accuracy of different approximation schemes.