Non-linear responses and three-particle correlators in correlated electron systems exemplified by the Anderson impurity model

TL;DR

This paper develops a formalism for three-particle correlators in correlated electron systems and demonstrates their significance through numerical analysis of the Anderson impurity model, highlighting the importance of full three-particle vertex corrections.

Contribution

It introduces a general formalism for three-particle correlators and shows their critical role in accurately describing responses in the Anderson impurity model.

Findings

Genuine three-particle vertex corrections are significant.

Bare bubble and two-particle vertex corrections are insufficient.

Full three-particle vertex must be included for accuracy.

Abstract

Three-particle correlators are relevant for, among others, Raman, Hall and non-linear responses. They are also required for the next order of approximations extending dynamical mean-field theory diagrammatically. We present a general formalism on how to treat these three-particle correlators and susceptibilities, and calculate the local three-particle response of the Anderson impurity model numerically. We find that genuine three-particle vertex corrections are sizable. In particular, it is not sufficient to just take the bare bubble terms or corrections based on the two-particle vertex. The full three-particle vertex must be considered.