Simulating Correlations with Computers Modeling and Simulation

0553891 - FZÚ 2022 RIV DE eng M - Monography Chapter
Janiš, Václav
Green functions in the renormalized many-body perturbation theory.
Simulating Correlations with Computers Modeling and Simulation. Jülich: Verlag des Forschungszentrum Jülich, 2021 - (Pavarini, E.; Koch, E.), s. 7.2-7.29. ISBN 978-3-95806-529-1
R&D Projects: GA ČR GA19-13525S
Institutional support: RVO:68378271
Keywords : strongly correlated electrons * renormalized many-body perturbation theory * two-particle self-consistency * screened effective interaction
OECD category: Condensed matter physics (including formerly solid state physics, supercond.)
https://www.cond-mat.de/events/correl21/manuscripts/correl21.pdf

I review how renormalizations are introduced in the quantum many-body perturbation theory. The one-particle renormalizations are discussed within the Baym-Kadanoff construction. We point to an inherent dichotomy of the Baym-Kadanoff approach in the relation between one and two-particle Green functions. They are the Schwinger-Dyson equation and the Ward identity that cannot be satisfied simultaneously in any approximate theory. I further introduce the two-particle approach with two-particle renormalizations that offers a way to reconcile the the two relations. Finally, I discuss a static mean-field-like approximation with a renormalized effective interaction determined self-consistently in the reduced parquet equations that leads to a qualitatively correct description of strong electron correlations in impurity and lattice models.
Permanent Link: http://hdl.handle.net/11104/0328586