Exact solution of a one-dimensional multicomponent lattice gas with hyperbolic interaction.

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse-sinh-square of the distance. This interaction contains a variable range as a parameter, and can thus interpolate between the known solutions for the nearest-neighbor chain, and the inverse-square chain. The energy, susceptibility, charge stiffness and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions. 03.65.Db Typeset using REVTEX 1 I. THE LATTICE MODEL FROM THE EXCHANGE MODEL In a recent Physical Review Letter [1], to be called S2, Sutherland and Shastry introduced a one-dimensional, continuum, multi-component quantum many-body system with a hyperbolic exchange interaction, governed by the following Hamiltonian: Hcont = − 1 2 ∑