Diagrammatic Monte Carlo study of quasi-two-dimensional Fermi-polarons

TL;DR

This study uses diagrammatic Monte Carlo to analyze Fermi-polarons in quasi-two-dimensional systems, revealing that higher-order particle-hole contributions cancel out, simplifying the understanding of polaron-molecule transitions.

Contribution

It demonstrates that in quasi-2D Fermi-polaron systems, higher-order particle-hole diagrams are negligible, aligning the results with pure 2D models and wave-function approaches.

Findings

Higher-order particle-hole contributions are negligible due to destructive interference.

The polaron-molecule transition in quasi-2D matches the pure 2D case.

Results agree with wave-function approach in the two-particle-hole subspace.

Abstract

We apply a diagrammatic Monte Carlo method to the problem of an impurity interacting resonantly with a homogeneous Fermi bath for a quasi-two-dimensional setup. Notwithstanding the series divergence, we can show numerically that the three particle-hole diagrammatic contributions are not contributing significantly to the final answer, thus demonstrating a nearly perfect destructive interference of contributions in subspaces with higher-order particle-hole lines. Consequently, for strong enough confinement in the third direction, the transition between the polaron and the molecule ground state is found to be in good agreement with the pure two-dimensional case and agrees very well with the one found by the wave-function approach in the two-particle-hole subspace.