Cumulant expansion in the Holstein model: Spectral functions and mobility

We examine the range of validity second-order cumulant expansion (CE) for calculation spectral functions, quasiparticle properties, and mobility Holstein polaron. devise an efficient numerical implementation that allows us to make comparisons in a broad interval temperature, electron-phonon coupling, phonon frequency. For benchmark, we use dynamical mean-field theory (DMFT) which gives, as have recently shown, rather accurate functions whole parameter space, even low dimensions. find one dimension, CE resolves well both first satellite peak regime intermediate coupling. At high temperatures, charge assumes power law $\mu\propto T^{-2}$ limit weak coupling T^{-3/2}$ stronger that, gives slightly better results than self-consistent Migdal approximation (SCMA), while one-shot is appropriate only very interaction. also analyze atomic sum rules. derive analytical expression moments they are exact up fourth order, opposed SCMA where third order. Finally, higher