Hierarchy wave functions--from conformal correlators to Tao-Thouless states

Abstract

Laughlin's wave functions, describing the fractional quantum Hall effect at filling factors $\nu =1/(2k+1)$, can be obtained as correlation functions in conformal field theory, and recently this construction was extended to Jain's composite fermion wave functions at filling factors $\nu =n/(2kn+1)$. Here we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multi-hole states, make the connection to Wen's general classification of abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally we discuss to what extent our wave functions can be described in the language of composite fermions.

9 pages

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Cited by in corpus (24)

• Quantum Hall Physics - hierarchies and CFT techniques
• Quantum Hall quasielectron operators in conformal field theory
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Hall Viscosity of Hierarchical Quantum Hall States
• Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations
• Quantum Hall quasielectrons - Abelian and non-Abelian
• Composite Fermions on a Torus
• Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
• Zero modes, Bosonization and Topological Quantum Order: The Laughlin State in Second Quantization
• Quasihole condensates in quantum Hall liquids
• Algebraic approach to the study of zero modes of Haldane pseudopotentials
• Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• Composite Fermion states on the torus
• The quantum Hall hierarchy in spherical geometry
• A general approach to quantum Hall hierarchies
• S3 Quantum Hall Wavefunctions
• Multi-Particle Pseudopotentials for Multi-Component Quantum Hall Systems
• Composite fermion model for entanglement spectrum of fractional quantum Hall states
• Fractional Quantum Hall Matrix Product States For Interacting Conformal Field Theories
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Transition from two-component 332 Halperin state to one-component Jain state at filling factor ν=2/5
• The length scale measurements of the Fractional quantum Hall state on cylinder
• Fermionization, Triangularization and Integrability