Froehlich Polaron and Bipolaron: Recent Developments

TL;DR

This paper reviews recent advances in understanding Froehlich polarons and bipolarons, key quantum field problems involving a fermion interacting with a scalar Bose field, highlighting analytical and numerical progress since 1950.

Contribution

It provides a comprehensive overview of recent developments, including new analytical and numerical techniques applied to continuum and lattice Froehlich (bi)polarons.

Findings

Advances in path integral and variational methods

Improved quantum Monte Carlo simulations

New insights into strong-coupling regimes

Abstract

It is remarkable how the Froehlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical solution at all coupling since 1950, when its Hamiltonian was first written. The field has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalisation (ED), and quantum Monte Carlo (QMC) techniques. This article reviews recent developments in the field of continuum and discrete (lattice) Froehlich (bi)polarons starting with the basics and covering a number of active directions of research.