# Multiloop functional renormalization group that sums up all parquet diagrams

## TL;DR

This paper introduces a multiloop functional renormalization group method that efficiently sums all parquet diagrams, significantly improving the accuracy of four-point vertex and self-energy calculations in many-body physics.

## Contribution

The authors develop a multiloop fRG flow that sums all parquet diagrams, providing a more accurate and comprehensive approach compared to traditional one-loop methods.

## Key findings

- Multiloop fRG sums all parquet diagrams to arbitrary order.
- Numerical results demonstrate equivalence to solving parquet equations.
- Method improves accuracy of self-energy calculations.

## Abstract

We present a multiloop flow equation for the four-point vertex in the functional renormalization group (fRG) framework. The multiloop flow consists of successive one-loop calculations and sums up all parquet diagrams to arbitrary order. This provides substantial improvement of fRG computations for the four-point vertex and, consequently, the self-energy. Using the X-ray-edge singularity as an example, we show that solving the multiloop fRG flow is equivalent to solving the (first-order) parquet equations and illustrate this with numerical results.