Normal state of highly polarized Fermi gases: Full many-body treatment

TL;DR

This paper provides an exact many-body analysis of a single impurity in a Fermi sea, explaining the success of simpler models through destructive interference of multi-particle-hole states.

Contribution

It demonstrates that considering only single particle-hole excitations suffices due to destructive interference, leading to an exact solution of the impurity problem.

Findings

Single particle-hole approximation agrees well with exact results.

Destructive interference explains the effectiveness of simplified models.

Two particle-hole calculations match known exact solutions.

Abstract

We consider a single \down atom within a Fermi sea of \up atoms. We elucidate by a full many-body analysis the quite mysterious agreement between Monte-Carlo results and approximate calculations taking only into account single particle-hole excitations. It results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. This is linked to the remarkable efficiency of the expansion in powers of hole wavevectors, the lowest order leading to perfect interference. Going up to two particle-hole pairs gives an essentially perfect agreement with known exact results. Hence our treatment amounts to an exact solution of this problem.