Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions
Abstract
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 duality between the differential equations fixing the electron and quasihole wavefunctions. They both satisfy the Laplace-Beltrami equation. We use this equation to obtain an analytic expression for the generic wavefunction with one excess flux. These results also apply to the more general models WA_{k-1}(k+1,k+r) corresponding to the recently introduced Jack states.
Cite
@article{arxiv.1005.3475,
title = {Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions},
author = {Benoit Estienne and B. Andrei Bernevig and Raoul Santachiara},
journal= {arXiv preprint arXiv:1005.3475},
year = {2013}
}