Non abelian fractional quantum Hall fluids

Full text: The fractional quantum Hall effect has led to the identification of new states of matter, which can be characterized as incompressible quantum fluids with off diagonal long-range order ('topological order'). After the initial discovery of the 'principal Laughlin series' of quantum Hall fluids at filling factor 1/m, a large class of so-called Abelian quantum Hall fluids has been identified, accounting for the rich spectrum of fractional quantum Hall plateaus that have been observed in the lowest Landau level. The observation of a quantum Hall plateau at filling factor 5/2 has made it clear that the traditional set of Abelian quantum Hall states will not suffice for explaining the phenomena observed in the second Landau level. Prompted by this development, new categories of incompressible quantum fluids have been proposed. The quasiparticles over these states satisfy what is called non-Abelian exclusion statistics. The topological order of fractional quantum Hall fluids can be characterized by a so-called K-matrix. Many of the low energy characteristics of the quantum Hall fluid, such as the filling factor and the spin Hall conductance, are encoded in this K-matrix and the quantum numbers of the elementary electron-type excitations. By studying the exclusion statistics properties of edge-electrons and edge-quasiholes, we arrive at a novel K-matrix structure. Interestingly, the duality between the electron and quasihole sectors links the pseudoparticles that are characteristic for non-Abelian statistics with composite particles that are associated to the 'pairing physics' of the non-Abelian quantum Hall states