On the validity of the Franck-Condon principle in the optical spectroscopy: optical conductivity of the Fröhlich polaron

Abstract

The optical absorption of the Fröhlich 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 ($α>10$); ii) a Memory Function Formalism with phonon broadened levels reproduces the optical response for weak coupling strengths ($α<6$) taking the dynamic lattice relaxation into account. In the coupling regime $6<α<10$ the optical conductivity is a rapidly changing superposition of both Franck-Condon and dynamic contributions.