Cooperative ring exchange theory of the fractional quantized Hall effect

A semiclassical path-integral approach is used to calculate the contribution of large correlated ring exchanges to the energy of a two-dimensional Wigner crystal in a strong magnetic field. This correlation energy Ec(ν) shows cusps at fractional fillings νc=n/m of the lowest Landau level. The uniform Wigner crystal is locally unstable for ν≠νc and the theory predicts the existence of fractionally charged quasiparticles to accommodate the extra density ν-νc.