Strongly correlated electrons: Dynamical vertex renormalization

TL;DR

This paper develops a simplified yet self-consistent approximation for the Hubbard model at criticality, incorporating dynamical vertex corrections to study two-particle singularities in strongly correlated electrons.

Contribution

It introduces a reduced parquet-based scheme focusing on key channels, enabling manageable analysis of two-particle correlations with dynamical vertex corrections.

Findings

The approximation captures dynamical vertex effects at the two-particle level.

It simplifies parquet equations to a form comparable with single-channel methods.

The approach provides a new way to analyze two-particle singularities at zero temperature.

Abstract

Single-band Hubbard model at criticality of the metal-insulator transition is studied using approximations derived from parquet theory. It is argued that only the electron-hole and interaction two-particle channels in the parquet algebra are relevant. A scheme is proposed how to reduce the parquet equations to a manageable form the complexity of which is comparable with single-channel approximations such as the renormalized RPA. The newly derived approximation, however, contains dynamical vertex corrections, remains self-consistent at the two-particle level and allows only for integrable singularities. A qualitatively new approach for studying two-particle singularities at zero temperature is obtained.