The anti-integrable limit of the Holstein model with a nonlinear phonon Hamiltonian: Localization properties

We have studied the dynamical properties of the Holstein model with a nonlinear phonon Hamiltonian. Using the translational invariance of the system we eliminate from the Hamiltonian the electronic degrees of freedom. The resulting Hamiltonian describes a displaced phonon variable coupled to a lattice of boson variables by means of an exchange term proportional to the electronic hopping integral. We show that in the anti-integrable limit, corresponding to small electronic hopping integral, the nonlinearity of the lattice potential has the effect of quenching the tunneling motion of the electron through the lattice. The possibility of localized excitations in the system is discussed. Copyright (C) 1998 Elsevier Science B.V.