Nature of the self-trapping transition in a one-dimensional Holstein-Hubbard model

Abstract

The nature of the self-trapping transition in a many-polaron system is investigated within the framework of an extended Holstein-Hubbard model in one dimension using a variational method. The phonon degrees of freedom are first eliminated employing a modified Lang-Firsov transformation and an onsite squeezing transformation and then using a correlated squeezed phonon state to yield an effective Hubbard model which is finally studied using the exact solution of Lieb and Wu and the mean-field Hartree-Fock approximation. It is shown that the exact solution of the effective Hubbard model predicts a smooth crossover from the large polaron to a small polaron state while the mean field treatment leads to a discontinuous transition in the adiabatic regime. © 2004 Elsevier B.V. All rights reserved.