Validity of the Franck-Condon Principle in the Optical Spectroscopy: Optical Conductivity of the Fröhlich Polaron

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 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.