Fermion-boson vertex within Dynamical Mean-Field Theory

TL;DR

This paper investigates the fermion-boson vertex in strongly correlated systems within Dynamical Mean-Field Theory, revealing its behavior across the metal-insulator transition and highlighting a divergence in the imaginary part.

Contribution

It provides a comprehensive analysis of the fermion-boson vertex using multiple theoretical tools and explores its critical behavior near the transition.

Findings

Divergence in the imaginary part of the vertex at the transition

Multiple perspectives elucidate the vertex's properties

The study enhances understanding of two-particle correlations in DMFT

Abstract

In the study of strongly interacting systems, correlations on the two-particle level are receiving more and more attention. In this work, we study a particular two-particle correlation function: the fermion-boson vertex. It describes the response of the Green's function when an external field is applied and is an important ingredient of diagrammatic extensions of Dynamical Mean-Field Theory. We provide several perspectives on this object, using Ward identities, sum rules, perturbative analysis and asymptotic relations. We then use these tools to study the vertex across the doping-driven metal-insulator transition and find a divergence in the imaginary part.