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

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.

11 pages (incl. appendix), 4 figures

References in corpus (11)

• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Screening and Non-local Correlations in the Extended Hubbard Model from Self-Consistent Combined GW and Dynamical Mean Field Theory
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• Superconductivity, antiferromagnetism and phase separation in the two-dimensional Hubbard model: A dual-fermion approach
• Spectral Properties of Correlated Materials: Local Vertex and Non-Local Two-Particle Correlations from Combined GW and Dynamical Mean Field Theory
• Extended dynamical mean-field study of the Hubbard model with long range interactions
• Plasmons in strongly correlated systems: spectral weight transfer and renormalized dispersion
• Efficient implementation of the continuous-time hybridization expansion quantum impurity solver
• Collective Charge Excitations of Strongly Correlated Electrons, Vertex Corrections and Gauge Invariance
• The effect of six-point one-particle reducible local interactions in the dual fermion approach

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