Anyons, The Quantum Hall Effect and Two- Dimensional Superconductivity

We have studied the ground-state (GS) properties of fractional-statistics particles (anyons) by exact numerical solution for small systems. We have seen in our results (depending on the choice of parameters for the Hamiltonian) the fractional-statistics analogs of a number of well-known ground states for conventional particles, including particularly the quantum Hall state (which we relate to the observed ‘hierarchy’ states), and a superconducting GS, the latter being formed (for half-statistics particles or semions) by pairing. We suggest possible experimental signatures for distinguishing semion from fermion superconductors. We also directly test the ‘mean-field theory’ of statistics against our exact results, and find it to treat GS properties well.