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.

References in corpus (19)

• Fractional Quantum Hall States and Jack Polynomials
• Correlation functions in conformal Toda field theory I
• Correlation functions in conformal Toda field theory II
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Conformal invariance of chiral edge theories
• Topological Quantum Computing with Read-Rezayi States
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states
• Wavefunctions for topological quantum registers
• Critical curves in conformally invariant statistical systems
• Non-Abelian Quantum Hall States and their Quasiparticles: from the Pattern of Zeros to Vertex Algebra
• Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
• Domain walls, fusion rules and conformal field theory in the quantum Hall regime
• S3 Quantum Hall Wavefunctions
• Symmetric polynomials vanishing on the shifted diagonals and Macdonald polynomials
• Highest weight Macdonald and Jack Polynomials
• Quasiparticle spin from adiabatic transport in quantum Hall trial wavefunctions
• The W_k structure of the Z_k^(3/2) models

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• Construction of the edge states in fractional quantum Hall systems by Jack polynomial
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
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• Quantum Hall Edges with Hard Confinement: Exact Solution beyond Luttinger Liquid
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• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
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