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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. Here, we first present multiloop fRG flow equations [1] as a way of simulating all contributions of the six-point vertex that can be kept efficiently. The resulting flow consists of successive one-loop calculations and sums up a complete class of diagrams. This restores the independence of the results from the choice of regulator and enables improvement of many fRG computations. Second, we show how to derive the multiloop flow equations from the self-consistent parquet relations on an algebraic basis [2]. Using the X-ray-edge singularity as an example, we introduce the formalism and illustrate our findings with numerical results [3]. [1] F. B. Kugler and J. von Delft, PRB 97, 035162 (2018) [2] F. B. Kugler and J. von Delft, New J. Phys. 20, 123029 (2018) [3] F. B. Kugler and J. von Delft, PRL 120, 057403 (2018)

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Fabian Kugler, TU Muenchen
Seminar Room 0.03, ETP
Contact: Dominik Kiese