Multiloop functional renormalization group for general models

TL;DR

This paper introduces multiloop functional renormalization group flow equations for general fermionic models, improving numerical accuracy and connecting to parquet and Schwinger-Dyson equations.

Contribution

It generalizes previous fRG vertex flow equations by including multiloop corrections, enabling more precise and efficient computations for fermionic many-body problems.

Findings

Multiloop flow equations match parquet and Schwinger-Dyson solutions.

Enhanced numerical algorithms for fRG computations.

Corrected self-energy flow for complete diagram derivatives.

Abstract

We present multiloop flow equations in the functional renormalization group (fRG) framework for the four-point vertex and self-energy, formulated for a general fermionic many-body problem. This generalizes the previously introduced vertex flow [F. B. Kugler and J. von Delft, Phys. Rev. Lett. 120, 057403 (2018)] and provides the necessary corrections to the self-energy flow in order to complete the derivative of all diagrams involved in the truncated fRG flow. Due to its iterative one-loop structure, the multiloop flow is well-suited for numerical algorithms, enabling improvement of many fRG computations. We demonstrate its equivalence to a solution of the (first-order) parquet equations in conjunction with the Schwinger-Dyson equation for the self-energy.