Condensed-Matter Physics & Materials Science Seminar

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 [1]. On the one hand, this circumvents the reliance on higher-point vertices within fRG and equips the method with quantitative predictive power [2]. 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 [3]. Finally, we discuss applications to the 2D Hubbard model [4] and the combination of multiloop fRG with the dynamical mean-field theory. [1] F. B. Kugler and J. von Delft, arXiv:1807.02898 (2018) [2] F. B. Kugler and J. von Delft, PRB 97, 035162 (2018) [3] F. B. Kugler and J. von Delft, PRL 120, 057403 (2018) [4] A. Tagliavini, C. Hille, F. B. Kugler, S. Andergassen, A. Toschi, and C. Honerkamp, arXiv:1807:02697 (2018)