# Application of renormalized RPA to polarized Fermi gases

## TL;DR

This paper extends the particle-particle RPA method with a renormalization scheme to better predict critical polarization and other properties of polarized Fermi gases near unitarity at zero temperature.

## Contribution

It introduces a renormalized RPA approach with self-consistent occupation numbers, improving predictions over standard RPA for polarized Fermi gases.

## Key findings

- Critical polarization is more accurately predicted.
- Occupation numbers are determined self-consistently.
- The approach highlights some limitations of the method.

## Abstract

We consider a spin imbalanced Fermi gas at zero temperature in the normal phase on the BCS side of the BCS-BEC crossover and around unitarity. We compute the critical polarization for pairing, the correlated occupation numbers and the contact in an extension of particle-particle RPA (also called non self-consistent \textit{T}-matrix approach or ladder approximation). The so-called renormalized RPA consists in computing the \textit{T} matrix with self-consistently determined occupation numbers. The occupation numbers are determined either by keeping the self-energy only to first order or by resumming the Dyson equation. In this way, the result for the critical polarization, strongly overestimated in standard RPA, is clearly improved. We also discuss some problems of this approach.