Landau Level Mixing and the Ground State of the ν=5/2 Quantum Hall Effect

One of the most intriguing fractional Hall states was discovered at the half-filled first excited Landau level at total filling of 5/2. It is the strongest even-denominator gapped topological phase that has been observed in a single layer system. Numerical studies consistently indicate that the Moore-Read (Pfaffian) state is the underlying phase of the 5/2-effect. As a result, the interest in the 5/2-effect was intensified due to the exotic property of non-Abelian exchange statistics of the low-energy excitations. This talk will review these studies that include transitions to other phases at 5/2 filling, which lack topological order. In most of the initial numerical studies the inter-Landau-level excitations were ignored. Otherwise the particle-hole symmetry is spoiled. Under these circumstances there are two equally likely yet topologically distinct phases of matter for the 5/2-effect. The two competing states are the Pfaffian and its particle-hole conjugate the so-called anti-Pfaffian. The ubiquity of the inter-Landau-level transitions (or mixing) in experiment breaks particle-hole symmetry of an isolated half-filled Landau level and will favor one or the other. More recent studies that addressed mixing effects yielded, depending on the method of approach, opposite predictions. The discrepancy, however, will be shown to disappear if sufficient numbers of 3-body pseudo-potentials are included in the effective Hamiltonian.