Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional

TL;DR

This paper introduces an atomic approximation of a four-particle irreducible functional to improve the dynamical mean field theory for strongly correlated systems near a Mott transition, capturing both weak and strong coupling regimes.

Contribution

It develops a novel atomic-limit approximation of a four-particle irreducible functional that self-consistently determines the impurity interaction, extending DMFT and DΓA methods.

Findings

Interpolates between parquet approximation and atomic limit

Applicable to systems with short- and long-range interactions

Self-consistent determination of impurity interactions

Abstract

We discuss a generalization of the dynamical mean field theory (DMFT) for strongly correlated systems close to a Mott transition based on a systematic approximation of the fully irreducible four-point vertex. It is an atomic-limit approximation of a functional of the one- and two-particle Green functions, built with the second Legendre transform of the free energy with respect to the two-particle Green function. This functional is represented diagrammatically by four-particle irreducible (4PI) diagrams. Like the dynamical vertex approximation (D$\Gamma$A), the fully irreducible vertex is computed from a quantum impurity model whose bath is self-consistently determined by solving the parquet equations. However, in contrast with D$\Gamma$A and DMFT, the interaction term of the impurity model is also self-consistently determined. The method interpolates between the parquet approximation at weak coupling and the atomic limit, where it is exact. It is applicable to systems with short-range and long-range interactions.