Probing the CORE of the Haldane Conjecture

The COntractor REnormalization group method (CORE), originally developed for application to lattice gauge theories, is very well adapted the study of spin systems and systems with fermions. As an warmup exercise for studying Hubbard models this method is applied to spin-1/2 and spin-1 anti-ferromagnets in one space dimension in order to see if it is able to explain the physics of the Haldane conjecture. The method not only provides support for Haldane's conjecture but provides insight into the physics of a more general class of spin-1 systems with Hamiltonians of the form $H= \sum_j \vec{s}(j)\cdot\vec{s}(j+1) - \beta (\vec{s}(j)\cdot\vec{s}(j+1))^2$ about which, until now, little was known.