Abstract
The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is solved by using a Bethe ansatz in analogue to that for the one-dimensional spinless Fermi?Hubbard model. Excitation energies and the corresponding wavefunctions of the model are determined by a set of partial differential equations. It is shown that the model is, at least, quasi-exactly solvable for the two-site case, when the phonon frequency, the electron?phonon coupling strength and the hopping integral satisfy certain relations. As examples, some quasi-exact solutions of the model for the two-site case are derived.
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