Abstract
The two-site Holstein model is studied by the analytical method of the coherent-state expansion. We obtain the recursive relationship among the expansion coefficients, which leads to the exact solutions of the eigenstate properties. The exact ground-state results in the whole coupling strength region and from antiadiabatic to adiabatic limits are in perfect agreement with that available by the exact numerical diagonalization technique. Comparison with the best perturbation results shows the success and shortcoming of the perturbative method. The coherent-state expansion method is a promising approach in studying electron-phonon $(e\ensuremath{-}\mathrm{ph})$ coupling systems.
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