Variational approaches to quantum impurities: from the Fr\"{o}hlich polaron to the angulon

TL;DR

This paper introduces new variational methods for quantum impurity problems, specifically applied to the Fröhlich polaron and angulon, and benchmarks their accuracy against existing theories across different coupling strengths.

Contribution

The paper presents novel variational approaches for quantum impurities and demonstrates their effectiveness on polarons and angulons, expanding computational tools in this field.

Findings

New variational methods accurately model impurity-bath interactions.

Approaches perform well across a range of coupling strengths.

Benchmarking shows improved or comparable accuracy to existing theories.

Abstract

Problems involving quantum impurities, in which one or a few particles are interacting with a macroscopic environment, represent a pervasive paradigm, spanning across atomic, molecular, and condensed-matter physics. In this paper we introduce new variational approaches to quantum impurities and apply them to the Fr\"{o}hlich polaron -- a quasiparticle formed out of an electron (or other point-like impurity) in a polar medium, and to the angulon -- a quasiparticle formed out of a rotating molecule in a bosonic bath. We benchmark these approaches against established theories, evaluating their accuracy as a function of the impurity-bath coupling.