Conformal field theory construction for nonabelian hierarchy wave functions

TL;DR

This paper constructs and analyzes nonabelian fractional quantum Hall wave functions using conformal field theory, revealing their topological properties and nonabelian fusion rules, with potential relevance to experimental states.

Contribution

It introduces a conformal field theory framework for nonabelian hierarchy wave functions, extending the understanding of topological orders in fractional quantum Hall systems.

Findings

Quasiparticles obey nonabelian su(q)_k fusion rules

Explicit wave functions for various topological orders

Conformal field theory description for braiding properties

Abstract

The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular nonabelian ones. Here we analyze a class of nonabelian fractional quantum Hall model states which are generalizations of the abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey nonabelian fusion rules of type su(q)_k. For a subset of these states we are able to derive the conformal field theory description that makes the topological properties - in particular braiding - of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.