Two-site model and its relation to the polaron-crystal model

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Abstract
A symmetric two-site, one-electron model is treated within perturbation theory in electron wavefunction overlap from different sites. The significant role of the double degeneracy of levels in the unperturbed Hamiltonian is pointed out. It is shown that as a result of this the terms of the perturbative expansion for the correction to the energy of an unperturbed level produce different results depending on the parity of the order. Namely, even terms give rise to a level shift (an analog of the polaron shift in the polaron-crystal model), while odd terms result in splitting (an analog of the polaron band width). Also, the shift of the levels decreases with increasing vibronic coupling constant by a power law, and their splitting, exponentially. This is in full accord with the well-known results of small-radius polaron theory.

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