Validity of the Frank-Condon Principle in the Optical Spectrosopy: Optical Conductivity of the Frolich Polaron

The optical absorption of the Fro¨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 Franck-Condon principle, well describes the optical conductivity for large coupling strengths (>10); (ii) a memory function formalism with phonon broadened levels reproduces the optical response for weak coupling strengths (<6) taking the dynamic lattice relaxation into account. In the coupling regime 6<<10, the optical conductivity is a rapidly changing superposition of both Franck-Condon and dynamic contributions.