Electron-quasihole duality and second-order differential equation for Read-Rezayi and Jack wave functions

Benoit Estienne, B. Andrei Bernevig, Raoul Santachiara

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9 Scopus citations

Abstract

We consider the quasihole wave functions of the non-Abelian Read-Rezayi quantum-Hall states which are given by the conformal blocks of the minimal model WAk-1 (k+1,k+2) of the WAk-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 wave function. We find a duality between the differential equations fixing the electron and quasihole wave functions. They both satisfy the Laplace-Beltrami equation. We use this equation to obtain an analytic expression for the generic wave function with one excess flux. These results also apply to the more general models WAk-1 (k+1,k+r) corresponding to the recently introduced Jack states.

Original languageEnglish (US)
Article number205307
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume82
Issue number20
DOIs
StatePublished - Nov 8 2010

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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