ANTIFERROMAGNETISM AND SPIN-WAVES IN THE HUBBARD-MODEL AT HALF-FILLING

For a localized quantum spin system, such as the Heisenberg model, one believes that the collective excitations will be gapless if the ground state is antiferromagnetic, by the spin-wave theory. In this paper, we use some rigorous results of Lieb and show that the above conclusion still holds for the Hubbard model at half-filling, which is an itinerant electron system.