A New Variational Study for Two-Site Holstein Model

A variational approach is developed to study the groundstate (GS) of thetwo-site Holstein model. By the extended coherent state, where the morephonon correlations are easily incorporated, we can get the very accurate ground state energy for all electron-phonon coupling range in typical values of hopping integral t=0.5,1.1, and 2.1 (in units of phonon frequency ω₀), which covers the crossover region fromantiadiabatic limit to the adiabatic limit. Within a very wide trange [0,2.7], the exact results for the GS energy are obtainedwith the twelfth (fourteenth) order corrections to the zeroth order wavefunction. Moreover, the present approach is more concise than anyother analytical ones in this field, and hopefully can be easilygeneralized to many other Holstein models.