The effect of six-point one-particle reducible local interactions in the dual fermion approach

TL;DR

This paper extends the dual fermion approach for strongly correlated systems by including six-point and higher order vertices, highlighting their importance for diagrammatic consistency and non-local corrections.

Contribution

It introduces a formulation that incorporates one-particle reducible six-point vertices into the dual fermion approach, emphasizing their role in ensuring diagrammatic consistency and accurate non-local corrections.

Findings

Six-point vertices are crucial for diagrammatic consistency.

Neglecting higher order vertices can lead to inaccuracies.

Non-local corrections are significantly affected by these vertices.

Abstract

We formulate the dual fermion approach to strongly correlated electronic systems in terms of the lattice and dual effective interactions, obtained by using the covariation splitting formula. This allows us to consider the effect of six-point one-particle reducible interactions, which are usually neglected by the dual fermion approach. We show that the consideration of one-particle reducible six-point (as well as higher order) vertices is crucially important for the diagrammatic consistency of this approach. In particular, the relation between the dual and lattice self-energy, derived in the dual fermion approach, implicitly accounts for the effect of the diagrams, containing 6-point and higher order local one-particle reducible vertices, and should be applied with caution, if these vertices are neglected. Apart from that, the treatment of the self-energy feedback is also modified by 6-point and higher order vertices; these vertices are also important to account for some non-local corrections to the lattice self-energy, which have the same order in the local 4-point vertices, as the diagrams usually considered in the approach. These observations enlighten an importance of 6-point and higher order vertices in the dual fermion approach, and call for development of new schemes of treatment of non-local fluctuations, which are based on one-particle irreducible quantities.