Electron-quasihole duality and second-order differential equation for Read-Rezayi and Jack wave functions
- Institute for Theoretical Physics, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)
- Department of Physics, Princeton University, Princeton, New Jersey 08544 (United States)
- LPTMS, UMR 8626, CNRS-Universite Paris-Sud, Batiment 100, 91405 Orsay (France)
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 WA{sub k-1}(k+1,k+2) of the WA{sub 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 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 WA{sub k-1}(k+1,k+r) corresponding to the recently introduced Jack states.
- OSTI ID:
- 21502892
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, Vol. 82, Issue 20; Other Information: DOI: 10.1103/PhysRevB.82.205307; (c) 2010 The American Physical Society; ISSN 1098-0121
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CONFORMAL INVARIANCE
DIFFERENTIAL EQUATIONS
DUALITY
ELECTRONS
HALL EFFECT
QUANTUM FIELD THEORY
SIMULATION
WAVE FUNCTIONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
LEPTONS