Quantum Antiferromagnets, Fractional Quantum Hall Effect.

Yu. E. Lozovik, O. I. Notych

Allan H. MacDonald

S. M. Girvin, Daniel P. Arovas

Using an idea of Rommelse and den Nijs, we have investigated a direct analogy between the topological order in integer quantum antiferromagnets and the topological order in the fractional quantum Hall effect (FQHE). Numerical results are presented for the S = 1 generalized Heisenberg chain. The analogy between the Laughlin gap in the FQHE and the Haldane gap in integer spin chains is discussed.

Robert Joynt

Daniel P. Arovas, Assa Auerbach

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.

R. Morf