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

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.