LOCALIZED VERSUS DELOCALIZED GROUND-STATES OF THE SEMICLASSICAL HOLSTEIN HAMILTONIAN

We carry out a numerical analysis of the semiclassical Holstein Hamiltonian describing the transport of a quasiparticle in a one-dimensional crystal with N sites. The quasiparticle, whose intersite interaction is V, is coupled with a coupling constant g to the lattice vibrations, whose maximum frequency is 2omega. We find that the character of the ground state is determined by two quantities: upsilon = V/g2omega and N. Specifically, there is a threshold value of upsilon beyond which the single-particle ground state is delocalized. The threshold is dependent on N. As N --> infinity, the threshold value of upsilon becomes infinite signifying that for reasonably sized crystals, the ground state is always localized. Our analysis supports some earlier conjectures.