Thermodynamic consistency of the charge response in dynamical mean-field based approaches

TL;DR

This paper investigates the conditions under which the charge response function remains thermodynamically consistent in dynamical mean-field theory and its extensions, highlighting the importance of vertex corrections and impurity correlations.

Contribution

It proves that static, homogeneous DMFT susceptibility is consistent with vertex corrections, and analyzes the conditions for consistency in EDMFT and dual boson approaches.

Findings

DMFT susceptibility is consistent with vertex corrections.

Dual boson approach closely approximates thermodynamic consistency.

EDMFT is only consistent in strongly correlated, near half-filling regimes.

Abstract

We consider the thermodynamic consistency of the charge response function in the (extended) Hubbard model. In DMFT, thermodynamic consistency is preserved. We prove that the static, homogeneous DMFT susceptibility is consistent as long as vertex corrections obtained from the two-particle impurity correlation function are included. In presence of a nonlocal interaction, the problem may be treated within extended DMFT (EDMFT), or its diagrammatic extension, the dual boson approach. We show that here, maintaining thermodynamic consistency requires knowledge of three- and four-particle impurity correlation functions, which are typically neglected. Nevertheless, the dual boson approximation to the response is remarkably close to consistency. This holds even when two-particle vertex corrections are neglected. EDMFT is consistent only in the strongly correlated regime and near half-filling, where the physics is predominantly local.