Harmonic expansion of the effective potential in Functional Renormalization Group at finite chemical potential

TL;DR

This paper introduces a harmonic expansion method to solve the Functional Renormalization Group equations at finite chemical potential, enabling the analysis of phase diagrams in Yukawa-type models.

Contribution

The paper presents a novel harmonic basis expansion technique to solve FRG equations at finite chemical potential, improving analysis of phase transitions.

Findings

Bosonic fluctuations weaken the phase transition

Method accurately maps FRG equations on a finite domain

Phase diagram of a Yukawa model was successfully determined

Abstract

In this paper we propose a method to study the Functional Renormalization Group at finite chemical potential. The method consists of mapping the FRG equations within the Fermi surface into a differential equation defined on a rectangle with zero boundary conditions. To solve this equation we use an expansion of the potential in a harmonic basis. With this method we determined the phase diagram of a simple Yukawa-type model; as expected, the bosonic fluctuations decrease the strength of the transition.