Quantum Hall hierarchy wave functions from conformal field theory

Susanne Viefers

University of Oslo

Wednesday, 14 January 2009, 13:30
Matfys library

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.