Role of three-particle vertex within dual fermion calculations

TL;DR

This paper explores the impact of including three-particle vertices in dual fermion calculations for the Hubbard model, revealing their significance in certain parameter regimes and their influence on high-frequency self-energy behavior.

Contribution

It introduces the calculation of the local three-particle vertex and assesses its effect on self-energy corrections beyond standard dual fermion theory.

Findings

Three-particle vertex corrections are small where two-particle corrections are small.

In some parameter regions, three-particle corrections are comparable to two-particle ones.

High-frequency self-energy behavior is dominated by three-particle vertex corrections.

Abstract

We investigate the influence of self-energy diagrams beyond the two-particle vertex level within dual fermion theory. Specifically, we calculate the local three-particle vertex and construct from it selected dual fermion self-energy corrections to dynamical mean field theory. For the two-dimensional Hubbard model, the thus obtained self-energy corrections are small in the parameter space where dual fermion corrections based on the two-particle vertex only are small. However, in other parts of the parameter space, they are of a similar magnitude and qualitatively different from standard dual fermion theory. The high-frequency behaviour of the self-energy correction is - surprisingly - even dominated by corrections stemming from the three-particle vertex.