Local Electronic Correlation at the Two-Particle Level

TL;DR

This paper analyzes local two-particle Green's functions and vertices within DMFT for the Hubbard model, providing insights into their frequency structures and implications for non-local correlations.

Contribution

It presents a unified diagrammatic formalism for analyzing local two-particle vertex functions in DMFT, including their interpretation and relation to perturbation theory and atomic limit.

Findings

Frequency structures of vertex functions are characterized.

Comparison with atomic limit clarifies vertex behavior.

Mapping onto attractive Hubbard model offers additional insights.

Abstract

Electronic correlated systems are often well described by dynamical mean field theory (DMFT). While DMFT studies have mainly focused hitherto on one-particle properties, valuable information is also enclosed into local two-particle Green's functions and vertices. They represent the main ingredient to compute momentum-dependent response functions at the DMFT level and to treat non-local spatial correlations at all length scales by means of diagrammatic extensions of DMFT. The aim of this paper is to present a DMFT analysis of the local reducible and irreducible two-particle vertex functions for the Hubbard model in the context of an unified diagrammatic formalism. An interpretation of the observed frequency structures is also given in terms of perturbation theory, of the comparison with the atomic limit, and of the mapping onto the attractive Hubbard model.