Self-Consistent Fluctuation Theory for Strongly Correlated Electron Systems

TL;DR

This paper introduces a self-consistent fluctuation theory for strongly correlated electrons using the Parquet formalism, capturing two-particle fluctuations and their impact on one-particle properties.

Contribution

It develops a novel self-consistent approach that constructs fully antisymmetric vertices for multiple fluctuation channels, ensuring Pauli principle compliance and improved modeling of correlated systems.

Findings

Eliminates magnetic instabilities via vertex renormalization in the spin channel.

Ensures the Mermin-Wagner theorem in models studied.

Reproduces critical exponents consistent with self-consistent renormalization theory.

Abstract

A self-consistent theory for two-particle fluctuations with renormalized irreducible vertices is proposed. Using the Parquet formalism, we construct the fully antisymmetric full vertex in terms of the two-particle fluctuations in the charge, the spin and the particle-particle channels on an equal footing to satisfy the Pauli principle. The fluctuations are determined self-consistently, which are reflected into the one-particle self-energy via the Schwinger-Dyson equation. We demonstrate the application of the present theory to the impurity Anderson model and the Hubbard model on a square lattice mainly for the particle-hole symmetric case. In both models the vertex renormalization in the spin channel eliminates magnetic instabilities of mean-field theory to ensure the Mermin-Wagner theorem. The present theory gives the same critical exponents of the self-consistent renormalization theory in the quantum critical region.