Lattice gas with nearest-neighbor interaction in one dimension with arbitrary statistics

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Abstract
We define a quantum lattice gas with arbitrary statistics. For a one‐dimensional system with nearest‐neighbor interaction, we show that the problem is exactly soluble by use of Bethe's hypothesis when the interaction Δ=±1. The ground state energy is then obtained for the fermions of spin 1/2. Two phases are found in the case Δ=‐1.