Extended Heisenberg models of antiferromagnetism: Analogies to the fractional quantum Hall effect

The ‘‘valence-bond’’ ground states for extended Heisenberg models discussed by Affleck et al. are shown to be of a Jastrow form. We discuss a striking analogy between these models and the ‘‘truncated pseudopotential’’ approach to the fractional quantum Hall effect. The valence-bond states are in analogy to the Laughlin ground state, and the magnon spectrum is deduced by use of a single-mode approximation.