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arXiv · 1005.3475

Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions

Benoit Estienne·B. Andrei Bernevig·Raoul Santachiara
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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.

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Benoit Estienne, B. Andrei Bernevig, Raoul Santachiara. 2010-05-19. Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions. https://doi.org/10.1103/physrevb.82.205307

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