A new numerical method is proposed for determining the low-frequency dynamics of the charge carrier coupled to the deformable quantum lattice. As an example, the polaron band structure is calculated for the one-dimensional Holstein model. The adiabatic limit on the lattice, which cannot be reached by other approaches, is investigated. In particular, an accurate description is obtained of the crossover between quantum small adiabatic polarons, pinned by the lattice, and large adiabatic polarons, moving along the continuum as classical particles. It is shown how the adiabatic contributions to the polaron dispersion, involving spatial correlations over multiple lattice sites, can be treated easily in terms of coherent states.
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