Title: Irreducible vertex divergences in strongly correlated metallic systems : the case of the Anderson impurity model
Other Titles: Irreduzible Vertexdivergenzen in stark korrelierten metallischen Systemen: Der Fall des Anderson Impurity Modells
Language: English
Authors: Chalupa, Patrick 
Qualification level: Diploma
Advisor: Toschi, Alessandro  
Assisting Advisor: Gunacker, Patrik 
Issue Date: 2017
Number of Pages: 79
Qualification level: Diploma
Abstract: 
The recently discovered occurrence of multiple divergences in the irreducible vertex functions of strongly correlated electron models, poses serious problems to the state-of-the-art many-body theory. Dynamical mean-field theory (DMFT) calculations for the Hubbard model have shown several lines of divergences of the irreducible vertex function, surrounding the Mott-Hubbard metal-insulator transition, a clear hint of a highly non-perturbative origin. At high temperatures/large interaction (U), where the Hubbard model approaches the atomic limit, the divergences could be ascribed to a unique underlying energy scale . This simple picture is however not applicable in the most interesting parameter regime of low temperatures and intermediate U, where the system behaves like a correlated Fermi-liquid metal. For this reason a simpler model was analysed, where a similar physics could be realized: the Anderson impurity model. This provides a more feasible way to treat the Fermi-liquid quasiparticle physics in the parameter regime of interest. In a preceding Projektarbeit I performed CT-HYB calculations at the two particle level, using w2dynamics. The results show the first divergence line for the Anderson impurity model, with an unexpected low temperature behaviour. Motivated by these preliminary findings, in this thesis an investigation of the whole phase diagram of the Anderson impurity model has been per- formed. In particular, using w2dynamics, additional lines of divergences were found: They could be classified in terms of the properties of their associated singular eigenvectors and compared with the corresponding ones found in other many-electron systems. This information provides novel insights on the physical mechanism underlying the breakdown of many-body perturbation theory, clarifying some aspects (such as the relation of the divergences with the Mott-Hubbard transition), which were not fully understood yet. In the final part of the master thesis the implication of the low-temperature behaviour of the divergence lines in the Anderson impurity model onto other models (such as the Hubbard) is discussed as well.
Keywords: elektronische Korrelation; Versagen der Vielteilchentheorie; Zweiteilchenkorrelationsfunktionen; Fermiflüssigkeitstheorie; Mott-Hubbard Übergang; Anderson Impurity Modell
electronic correlations; breakdown of many-body theory; two particle correlation functions; Fermi liquid theory; Mott Hubbard transitions; Anderson impurity model
URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-100961
http://hdl.handle.net/20.500.12708/9813
Library ID: AC13753159
Organisation: E138 - Institut für Festkörperphysik 
Publication Type: Thesis
Hochschulschrift
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