Functional renormalization group with counterterms for competing order parameters

TL;DR

This paper introduces a method using symmetry-breaking counterterms within the fermionic functional renormalization group to accurately determine phase boundaries in systems with competing orders, overcoming divergences in RG flows.

Contribution

It proposes a novel approach employing symmetry-breaking counterterms and self-consistency conditions to improve phase diagram calculations in fermionic systems with competing instabilities.

Findings

Phase boundaries are accurately reproduced in 1D systems.

The method overcomes divergences in RG flows.

Encourages application to higher-dimensional systems.

Abstract

We explore the possibilities of using the fermionic functional renormalization group to compute the phase diagram of systems with competing instabilities. In order to overcome the ubiquituous divergences encountered in RG flows, we propose to use symmetry breaking counterterms for each instability, and employ a self-consistency condition for fixing the counterterms. As a validity check, results are compared to known exact results for the case of one-dimensional systems. We find that whilst one-dimensional peculiarities, in particular algebraically decaying correlation functions, can not be reproduced, the phase boundaries are reproduced accurately, encouraging further explorations for higher-dimensional systems.