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An interacting spin-fermion model is exactly solved on an open chain. In acertain representation, it is the nearest-neighbor Hubbard model in the limitof infinite $U$ (local interaction). Exact solution of its complete energyeigen-spectrum is accomplished by introducing a unitary transformation whichmaps the original problem to a tight-binding model of the fermions only.Physically, the exact solution implies the absence of Nagaoka ferromagnetism inthe ground state for arbitrary electron densities. The present method solves aclass of very general models exactly. Few more problems are discussed as anapplication of this unitary transform method.

Exact solution of the infinite-U Hubbard problem and other models in one dimension