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 dynamical mean-field theory (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 the 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.
- Publication:
-
Physical Review B
- Pub Date:
- August 2015
- DOI:
- 10.1103/PhysRevB.92.085106
- arXiv:
- arXiv:1505.05305
- Bibcode:
- 2015PhRvB..92h5106V
- Keywords:
-
- 71.10.Fd;
- 71.30.+h;
- Lattice fermion models;
- Metal-insulator transitions and other electronic transitions;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 11 pages (incl. appendix), 4 figures