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Quantum Hall hierarchy wave functions from conformal field theory

### Susanne Viefers

University of Oslo

**Wednesday, 14 January 2009, 13:30**

Matfys library

**Abstract**:

It has long been known that Laughlin's wave functions, describing the
fractional quantum Hall effect at filling fractions v = 1/(2k +1), can
be obtained as correlation functions in conformal field theory. We show
how to generalize this approach to construct explicit trial wave
functions for all states in the quantum Hall hierarchy. At the special
filling fractions v = n/(2np + 1) and n/(2np - 1) this construction
exactly reproduces Jain's composite fermion wave functions. Our
construction can be used to prove that Jain's wave functions are, in
fact, hierarchical, thus settling an old controversy. Moreover, this
approach can be generalized to produce trial wave functions for the
non-Abelian quasielectron states of the Moore-Read Pfaffian.