Quasihole wavefunctions in non-Abelian fractional quantum Hall states: from conformal field theory to Calogero-Sutherland Hamiltonians
Benoit Estienne
Lundi 31/01/2011, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
We consider the quasihole wavefunctions of the non-abelian Read-Rezayi quantum Hall states which are given by the conformal blocks of the minimal model $WA_{k-1}(k+1, k+2)$ of the $WA_{k-1}$ algebra. By studying the degenerate representations of this conformal field theories, we derive a second order differential equation satisfied by a general many-quasihole wavefunction. We find a surprising duality between the differential equations fixing the electron and quasihole wavefunctions: they both satisfy a Calogero-Sutherland type equation. We use this equation to obtain an analytic expression for the generic wavefunction with one excess flux. This analysis also applies to the more general models $WA_{k-1}(k+1, k+r)$ corresponding to the recently introduced Jack states. These results hints at some novel structure about non polynomial solutions of Calogero-Sutherland Hamiltonian.
Contact : Vincent PASQUIER


Retour en haut