An all-coupling theory for the Fr\"ohlich polaron

TL;DR

This paper introduces an all-coupling renormalization group method to accurately describe Fr"ohlich polarons across all interaction strengths, including Bose polarons in ultracold gases, and benchmarks it against quantum Monte Carlo results.

Contribution

The paper presents a novel renormalization group approach capable of describing Fr"ohlich polarons in all coupling regimes, including the full phase diagram for Bose polarons with arbitrary impurity masses.

Findings

Accurately predicts ground state energies across all coupling regimes.

Provides the full phase diagram of the Bose polaron model.

Benchmarked successfully against diagrammatic quantum Monte Carlo calculations.

Abstract

The Fr\"ohlich model describes the interaction of a mobile impurity with a surrounding bath of phonons which leads to the formation of a quasiparticle, the polaron. In this article an efficient renormalization group approach is presented which provides a description of Fr\"ohlich polarons in all regimes ranging from weak- to strong coupling. We apply the method to the Bose polaron problem of an ultracold impurity atom interacting with a background gas that is Bose-condensed. The extended renormalization group approach introduced here is capable to predict ground state properties for arbitrarily small impurity masses. This allows us to obtain the full phase diagram of the corresponding Bogoliubov-Fr\"ohlich Hamiltonian, characterized by two dimensionless coupling constants. Our method is benchmarked by comparison of the ground state energy to recent diagrammatic quantum Monte Carlo calculations.