Journal of Statistical Physics, Vol. 52, Nos. 3/4, 1988. p. 627-638.
It is shown for a class of antiferromagnetic Hamiltonians how one can get lower bounds for the energy gap above the ground state by diagonalizing a finite system. This method is applied to certain spin chains (including a spin-1 chain). Trial wave functons are proposed for the elementary excitations and are tested in the case of the spin-1 chain.