Correlated starting points for the functional renormalization group

TL;DR

This paper introduces a general framework for extending functional renormalization group methods by starting from an exactly solvable interacting reference system, enabling non-perturbative inclusion of correlations.

Contribution

It develops a systematic expansion around a solvable reference, incorporating correlations non-perturbatively, and relates this to existing methods like DMFT, DMF$^2$RG, and dual-fermion formalism.

Findings

Derivation of flow equations for auxiliary fields using Hubbard-Stratonovich transformation.

Establishes the relation between the new approach and conventional weak-coupling truncation.

Demonstrates the framework with the dynamical mean-field theory as a reference system.

Abstract

We present a general frame to extend functional renormalization group (fRG) based computational schemes by using an exactly solvable interacting reference problem as starting point for the RG flow. The systematic expansion around this solution accounts for a non-perturbative inclusion of correlations. Introducing auxiliary fermionic fields by means of a Hubbard-Stratonovich transformation, we derive the flow equations for the auxiliary fields and determine the relation to the conventional weak-coupling truncation of the hierarchy of flow equations. As a specific example we consider the dynamical mean-field theory (DMFT) solution as reference system, and discuss the relation to the recently introduced DMF$^2$RG and the dual-fermion formalism.