One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT

TL;DR

This paper introduces a new 1PI functional approach that unifies and extends existing diagrammatic methods like DΓA and dual fermion schemes to include non-local correlations beyond DMFT.

Contribution

The paper develops a 1PI formalism that combines features of DΓA and dual fermion methods, including higher-order vertices and non-local correlations beyond DMFT.

Findings

The 1PI approach includes diagrams not in ladder DΓA.

Numerical results for the 2D Hubbard model show the approach's effectiveness.

Comparison of 1PI, DF, and DΓA clarifies their differences and similarities.

Abstract

We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length-scales beyond the local correlations of dynamical mean field theory (DMFT). This formalism allows us to unify aspects of the dynamical vertex approximation (D\GammaA) and the dual fermion (DF) scheme, yielding a consistent formulation of non-local correlations at the one- and two-particle level beyond DMFT within the functional integral formalism. In particular, the considered approach includes one-particle reducible contributions from the three- and more-particle vertices in the dual fermion approach, as well as some diagrams not included in the ladder version of D\GammaA. To demonstrate the applicability and physical content of the 1PI approach, we compare the diagrammatics of 1PI, DF and D\GammaA, as well as the numerical results of these approaches for the half-filled Hubbard model in two dimensions.