Nonperturbative Renormalisation Group: Applications to the few and many-body systems

TL;DR

This paper explores the use of functional renormalisation group methods to analyze both few-body and many-body fermionic systems, highlighting the impact of cutoff dependence and the benefits of including three-body interactions.

Contribution

It demonstrates the application of the functional renormalisation group to fermionic systems, showing how three-body terms reduce cutoff dependence and validating the method's reliability for many-body physics.

Findings

Cutoff dependence in two-body truncation is significant.

Adding three-body terms reduces cutoff dependence.

FRG provides reliable results for many-fermion systems.

Abstract

We consider the applications of functional renormalisation group to few and many-body systems. As an application to the few-body dynamics we study the ratio between the fermion-fermion scattering length and the dimer-dimer scattering length for systems of few nonrelativistic fermions. We find a strong dependence on the cutoff function used in the renormalisation flow for a two-body truncation of the action. Adding a simple three-body term substantially reduces this dependence. In the context of many-body physics we study the dynamics of both symmetric and asymmetric many-fermion systems using the same functional renormalisation technique. It is demonstrated that functional renormalisation group gives sensible and reliable results and provides a solid theoretical ground for the future studies. Open questions as well as lines of further developments are discussed.