A Unified Treatment for XXX-Heisenberg Model and Haldane-Shastry Model Using Shift Operators

A unified treatment is developed for the XXX-Heisenberg model and a long-ranged interaction model (the $H_2$ in Haldane-Shastry model) from the point of view of shift operators (or raising and lowering operators), based on which the energy spectra of the spin-chain models are determined. Some physical discussions are also made.