EXACT SOLUTION OF THE SMALL-POLARON PROBLEM IN INFINITE DIMENSIONS

The spectral function of a single electron coupled to Einstein phonons (Holstein model) is calculated exactly in the limit of large space dimensionality, for any coupling strength and phonon frequency. A self-consistent mapping onto an effective impurity model leads to the solution in terms of a continued-fraction expansion for the electron propagator at zero temperature. True self-trapping is obtained only for finite bandwidth, such as the case of a Bethe lattice in infinite dimensions. It is shown that at intermediate coupling multiphonon resonances develop, corresponding to polaron states. Only the lowest one has long lifetime, and the polaron mass is calculated.