Exact treatment of exciton-polaron formation by Diagrammatic Monte Carlo

TL;DR

This paper introduces an exact Diagrammatic Monte Carlo method to study exciton-polaron formation, providing precise results for their properties and analyzing the limitations of common approximations.

Contribution

Develops an approximation-free Diagrammatic Monte Carlo technique for fermionic interactions, applied to the exciton-polaron problem with comprehensive numerical results.

Findings

Exact wave function, energy, and mass of exciton-polaron obtained.

Instantaneous approximation is limited in applicability.

Heavy hole and light electron case approximates a particle in a static impurity field.

Abstract

We develop an approximation-free Diagrammatic Monte Carlo technique to study fermionic particles interacting with each other simultaneously through both an attractive Coulomb potential and bosonic excitations of the underlying medium. Exemplarily we apply the method to the long-standing exciton-polaron problem and present numerically exact results for the wave function, ground-state energy, binding energy and effective mass of this quasiparticle. Focusing on the electron-hole pair bound-state formation, we discuss various limiting cases of a generic exciton-polaron model. The frequently used instantaneous approximation to the retarded interaction due to the phonon exchange is found to be of very limited applicability. For the case of a light electron and heavy hole the system is well approximated by a particle in the field of a static attractive impurity.