###### Content

# Multiloop functional renormalization group that sums up all parquet diagrams

### Fabian Kugler

#### 25.04.2018 at 12:15

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 present multiloop fRG flow equations for the four-point vertex and the self-energy [1], which are based on the truncated fRG flow and further simulate the effect of the six-point vertex on parquet diagrams. The multiloop flow consists of successive one-loop calculations and sums up all parquet diagrams to arbitrary order, enabling improvement of many fRG computations. Using the X-ray-edge singularity as an example, we introduce the formalism and illustrate our findings with numerical results [2].

[1] F. B. Kugler and J. von Delft, PRB 97, 035162 (2018)

[2] F. B. Kugler and J. von Delft, PRL 120, 057403 (2018)

A 450, Theresienstr. 37