On the validity of the Franck-Condon principle in the optical spectroscopy: optical conductivity of the Fr\"{o}hlich polaron

TL;DR

This paper evaluates the applicability of the Franck-Condon principle to the optical spectroscopy of Fröhlich polarons, comparing it with other methods across different coupling strengths.

Contribution

It provides an approximation-free Monte Carlo benchmark and assesses the validity of Franck-Condon and other approximate approaches in various coupling regimes.

Findings

Franck-Condon principle accurately describes large coupling ($ extstyle extgreater 10$)

Memory Function Formalism captures weak coupling ($ extstyle extless 6$) behavior

Intermediate coupling ($6< extstyle extless 10$) involves mixed contributions

Abstract

The optical absorption of the Fr\"{o}hlich polaron model is obtained by an approximation-free Diagrammatic Monte Carlo method and compared with two new approximate approaches that treat lattice relaxation effects in different ways. We show that: i) a strong coupling expansion, based on the the Franck-Condon principle, well describes the optical conductivity for large coupling strengths ($\alpha >10$); ii) a Memory Function Formalism with phonon broadened levels reproduces the optical response for weak coupling strengths ($\alpha <6$) taking the dynamic lattice relaxation into account. In the coupling regime $6<\alpha<10$ the optical conductivity is a rapidly changing superposition of both Franck-Condon and dynamic contributions.