Condensed-Matter Physics & Materials Science Seminar
"Multiloop functional renormalization group: Exact flow equations from the self-consistent parquet relations"
Presented by Fabian Kugler, Ludwig-Maximilians-Universitat Munchen, Germany
Thursday, September 20, 2018, 1:30 pm — ISB 734 Conference Room 201
The functional renormalization group (fRG) is a versatile, quantum-field-theoretical formulation of the powerful RG idea and has seen a large number of successful applications. The main limitation of this framework is the truncation of the hierarchy of flow equations, where typically effective three-particle interactions are neglected altogether. From another perspective, the parquet formalism consists of self-consistent many-body relations on the one- and two-particle level and allows for the most elaborate diagrammatic resummations. Here, we unify these approaches by deriving multiloop fRG flow equations from the self-consistent parquet relations . On the one hand, this circumvents the reliance on higher-point vertices within fRG and equips the method with quantitative predictive power . On the other hand, it enables solutions of the parquet equations in previously unaccessible regimes. Using the X-ray-edge singularity as an example, we introduce the formalism and illustrate our findings with numerical results . Finally, we discuss applications to the 2D Hubbard model  and the combination of multiloop fRG with the dynamical mean-field theory.  F. B. Kugler and J. von Delft, arXiv:1807.02898 (2018)  F. B. Kugler and J. von Delft, PRB 97, 035162 (2018)  F. B. Kugler and J. von Delft, PRL 120, 057403 (2018)  A. Tagliavini, C. Hille, F. B. Kugler, S. Andergassen, A. Toschi, and C. Honerkamp, arXiv:1807:02697 (2018)
Hosted by: Andreas Weichselbaum
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