Exact solution of the Sutherland model with arbitrary internal symmetry

An elementary theory is presented for solving the Sutherland model with arbitrary internal symmetry such as SU(ν) or a supersymmetry SU(ν,μ). The ground-state wave function and all the energy levels are derived. One starts with solving a variant of the model with distinguishable particles, and then (anti)symmetrizes the solution. The theory is also applied to various lattice versions of the model. It is proved that the Gutzwiller-type wave function is not only an eigenstate of the supersymmetric t-J model, but is indeed the ground state.