Determining the validity of solutions of the meanfield Bogoliubov-de Gennes equation

TL;DR

This paper introduces a methodology to assess the validity of the meanfield Bogoliubov-de Gennes equation, revealing its limitations in describing FFLO states in imbalanced ultracold Fermi gases at finite temperatures.

Contribution

The paper develops a general approach to evaluate the applicability of the meanfield Bogoliubov-de Gennes equation, specifically applied to imbalanced ultracold Fermi gases.

Findings

Meanfield assumptions break down for FFLO states at finite temperatures.

The methodology identifies regimes where the Bogoliubov-de Gennes equation is invalid.

Results suggest caution when using meanfield theory for certain strongly interacting systems.

Abstract

We provide a general methodology to directly determine the validity of the meanfield Bogoliubov-de Gennes equation. In particular we apply this methodology to the case of two component interacting ultracold Fermi gases. As an example, we consider the case of population imbalance, between the two components, in the strongly attractive interacting regime, where meanfield results predict Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states. For these states we find at finite temperatures that the assumptions used to derive the Bogoliubov-de Gennes equation are invalid.