Dresden 2017 – scientific programme

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MA: Fachverband Magnetismus

MA 13: Transport: Topological Phases (jointly with DS, MA, HL, O)

MA 13.11: Talk

Monday, March 20, 2017, 17:45–18:00, HSZ 304

Properties of non-abelian hierarchy states in the fractional quantum Hall effect — •Yoran Tournois and Maria Hermanns — Institute for Theoretical Physics, Cologne, Germany

The fractional quantum Hall effect is one of the paradigmatic examples of topological order in condensed matter physics. While the physics of the fractional quantum Hall effect is well understood in the lowest Landau level by means of the Haldane-Halperin hierarchy, a general method to describe the properties of quantum Hall liquids in the second Landau level is lacking. These are of particular interest, as it is believed that they may harbor exotic excitations - non-abelian anyons. In this talk, we consider a general class of model wave functions, which were recently proposed as a generalization of the Haldane-Halperin hierarchy. While these are conjectured to describe non-abelian quantum Hall liquids, many of their properties are not manifest and thus previously unknown. We determine their properties using a variety of methods. In particular, we derive the explicit conformal field theory description of the model wave functions, which reveals the non-abelian braiding statistics of the quasiparticles as well as the edge theory.