Mean-field approximation for thermodynamic and spectral functions of correlated electrons: Strong-coupling and arbitrary band filling

TL;DR

This paper develops a mean-field theory for strongly correlated electrons that accurately predicts thermodynamic and spectral properties across various band fillings, using a self-consistent effective interaction derived from parquet equations.

Contribution

It introduces a novel static local approximation for the two-particle irreducible vertex, enabling a consistent and analytically controllable mean-field approach in the strong-coupling regime.

Findings

Successfully applied to the Anderson impurity model.

Accurately captures spectral functions in the Hubbard model.

Free of unphysical phase transitions.

Abstract

We present a construction of a mean-field theory for thermodynamic and spectral properties of correlated electrons reliable in the strong-coupling limit. We introduce an effective interaction determined self-consistently from the reduced parquet equations. It is a static local approximation of the two-particle irreducible vertex, the kernel of a potentially singular Bethe-Salpeter equation. The effective interaction enters the Ward identity from which a thermodynamic self-energy, renormalizing the one-electron propagators, is determined. The dynamical Schwinger-Dyson equation with the thermodynamic propagators is then used to calculate the spectral properties. The thermodynamic and spectral properties of correlated electrons are in this way determined on the same footing and in a consistent manner. Such a mean-field approximation is analytically controllable and free of unphysical behavior and spurious phase transitions. We apply the construction to the asymmetric Anderson impurity and the Hubbard models in the strong-coupling regime.