The CORE of the Haldane Conjecture

Sometimes, when carrying out a preliminary computation in order to be sure that well understood llimits of a problem are handled correctly, results which are interesting in their own right emerge. I will now discuss one such result which I have obtained as part of such a preliminary study of the Hubbard model. The Hubbard model at halflling is equivalent to a Heisenberg anti-ferromagnet (HAF) and it is important to show that CORE treats this limiit correctly. This was shown to be the case for the spin-1/2 HAF in Ref.[1]. What that paper did not address was the subtle question of how the physics of the one-dimensional anti-ferromagnet changes when the spin-1/2 on each lattice site is replaced by spin S. In 1983 it was argued by F.D.M. Haldane, Ref.[2] that when S is a halfinteger, then the spectrum has no mass-gap, but when S is an integer, a mass-gap develops. In this talk I describe a CORE computation for the spin1/2 and spin-1 anti-ferromagnet which not only supports Haldane's conjecture, but shows how the spin-1 case leads to an understanding of a more general class of theories de ned by a Hamiltonian of the form