  We present a detailed numerical study of the one-dimensional Holstein model
with a view to understanding the self-trapping process of electrons or excitons
in crystals with short-range particle-lattice interactions. Applying a very
efficient variational Lanczos method, we are able to analyze the ground-state
properties of the system in the weak-- and strong-coupling, adiabatic and
non-adiabatic regimes on lattices large enough to eliminate finite-size
effects. In particular, we obtain the complete phase diagram and comment on the
existence of a critical length for self-trapping in spatially restricted
one-dimensional systems. In order to characterize large and small polaron
states we calculate self-consistently the lattice distortions and the
particle-phonon correlation functions. In the strong-coupling case, two
distinct types of small polaron states are shown to be possible according to
the relative importance of static displacement field and dynamic polaron
effects. Special emphasis is on the intermediate coupling regime, which we also
study by means of direct diagonalization preserving the full dynamics and
quantum nature of phonons. The crossover from large to small polarons shows up
in a strong decrease of the kinetic energy accompanied by a substantial change
in the optical absorption spectra. We show that our numerical results in all
important limiting cases reveal an excellent agreement with both analytical
perturbation theory predictions and very recent density matrix renormalization
group data.
