We adapt a variational procedure to calculate ground state properties of the Holstein model in the adiabatic limit. At strong coupling, this adaption leads to rapid convergence of results. The intermediate coupling regime is further handled with an adaptive algorithm. We also use semi-classically derived results for the adiabatic end-point, along with weak coupling perturbation theory. These establish weak and strong coupling (or large and small polaron, respectively) regimes in two dimensions

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... r higher. As is well known, these are connected smoothly, but the cross-over becomes increasingly abrupt as the phonon frequency decreases.