Analytical Solutions of the Two-Site Holstein Model by the Coherent State Expansion

Abstract

The polaron problem presents a highly nonlinear dynamical system in which the charge and lattice deformations are intricately coupled together. The coherent state expansion method was applied to the two-site Holstein model. Analytical solutions are found for the first, the second and the third order approximations. Comparison is made among the exact numerical results, based upon solving a recursive relation for the expansion coefficients, and the analytical solutions up to the third order approximation for various e-ph coupling strengths and electron hopping parameters.