  An analytical approach to the one-dimensional spinless Holstein model is
proposed, which is valid at finite charge-carrier concentrations. Spectral
functions of charge carriers are computed on the basis of self-energy
calculations. A generalization of the Lang-Firsov canonical transformation
method is shown to provide an interpolation scheme between the extreme weak-
and strong-coupling cases. The transformation depends on a variationally
determined parameterthat characterizes the charge distribution across the
polaron volume. The relation between the spectral functions of polarons and
electrons, the latter corresponding to the photoemission spectrum, is derived.
Particular attention is paid to the distinction between the coherent and
incoherent parts of the spectra, and their evolution as a function of band
filling and model parameters. Results are discussed and compared with recent
numerical calculations for the many-polaron problem.
