Optical conductivity of the Holstein polaron

The Momentum Average approximation is used to derive a new kind of non-perturbational analytical expression for the optical conductivity (OC) of a Holstein polaron at zero temperature. This provides insight into the shape of the OC, by linking it to the structure of the polaron's phonon cloud. Our method works in any dimension, properly enforces selection rules, can be systematically improved, and also generalizes to momentum-dependent couplings. Its accuracy is demonstrated by a comparison with the first detailed set of three-dimensional numerical OC results, obtained using the approximation-free diagrammatic Monte Carlo method.