A variational method for many-body systems using a separation into a difference of Hamiltonians

A particular ansatz for the wave function leads to an upper bound for the exact ground-state energy. This allows a variation with respect to a separation parameter. The method is tested for a one-dimensional lattice with Morse interactions where the Toda subsystems can be solved by the Bethe ansatz. In two limiting cases our results are exact, otherwise they are in excellent agreement with the quantum transfer integral method