MANY-BODY SYSTEMS WITH NON-ABELIAN STATISTICS

We use conformal field theory to construct many-body hamiltonians whose ground states support quasiparticle excitations with non-abelian statistics. Explicit forms of the many-body ground-state wave functions are calculated. The above systems may appear naturally in the Fractional Quantum Hall Effect (FQHE) in the low-density limit. We discuss the calculation of quasiparticle statistics from the low-energy effective theory and from the microscopic wave function. The stability of the non-abelian statistics under small perturbations of the system is also considered. We argue that the non-abelian statistics is a topological property of the many-body systems. This property does not depend on the detailed short-ranged structures of the systems.