SELF-TRAPPING PROBLEM OF ELECTRONS OR EXCITONS IN ONE-DIMENSION

We present a detailed numerical study of the one-dimensional Holstein model with a view to understanding the self-trapping process of electr ons or excitons in crystals with short-range particle-lattice interact ions. Applying a very efficient variational Lanczos method, we are abl e to analyze the ground-state properties of the system in the weak- an d strong-coupling, adiabatic and nonadiabatic regimes on lattices larg e enough to eliminate finite-size effects. In particular, we obtain th e complete phase diagram and comment on the existence of a critical le ngth for self-trapping in finite (closed) one-dimensional systems. In order to characterize large and small polaron states we calculate self -consistently the lattice distortions and the particle-phonon correlat ion functions. In the strong-coupling case, two distinct types of smal l polaron states are shown to be possible according to the relative im portance of static displacement field and dynamic polaron effects. Spe cial emphasis is on the intermediate-coupling regime, which we also st udy by means of direct diagonalization, preserving the full dynamics a nd quantum nature of phonons. The crossover from large to small polaro ns shows up in a strong decrease of the kinetic energy accompanied by a substantial change in the optical absorption spectra. We show that o ur numerical results in all important Limiting cases reveal excellent agreement with both analytical perturbation theory predictions and ver y recent density matrix renormalization group data.