Clustering properties, Jack polynomials and unitary conformal field theories

Abstract

Recently, Jack polynomials have been proposed as natural generalizations of Z_k Read-Rezayi states describing non-Abelian fractional quantum Hall systems. These polynomials are conjectured to be related to correlation functions of a class of W-conformal field theories based on the Lie algebra A_{k-1}. These theories can be considered as non-unitary solutions of a more general series of CFTs with Z_k symmetry, the parafermionic theories. Starting from the observation that some parafermionic theories admit unitary solutions as well, we show, by computing the corresponding correlation functions, that these theories provide trial wavefunctions which satisfy the same clustering properties as the non-unitary ones. We show explicitly that, although the wavefunctions constructed by unitary CFTs cannot be expressed as a single Jack polynomial, they still show a fine structure where the mathematical properties of the Jack polynomials play a major role.

20 pages. Published version

References in corpus (17)

• Non-Abelian Anyons and Topological Quantum Computation
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Fractional Quantum Hall States and Jack Polynomials
• Topological Entanglement and Clustering of Jain Hierarchy States
• A nu=2/5 Paired Wavefunction
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
• Conformal invariance of chiral edge theories
• Generalized Quantum Hall Projection Hamiltonians
• 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
• Structure of Quasiparticles and Their Fusion Algebra in Fractional Quantum Hall States
• Domain walls, fusion rules and conformal field theory in the quantum Hall regime
• Correlators of N=1 Superconformal Currents

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• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Gapless excitations in the Haldane-Rezayi state: The thin torus limit
• The structure of spinful quantum Hall states: a squeezing perspective
• Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Entanglement subspaces, trial wavefunctions, and special Hamiltonians in the fractional quantum Hall effect
• S3 Quantum Hall Wavefunctions
• Jack polynomial fractional quantum Hall states and their generalizations
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
• Effective Edge State Dynamics in the Fractional Quantum Hall Effect
• Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions
• Quantum Hall Edges with Hard Confinement: Exact Solution beyond Luttinger Liquid
• Fractional Quantum Hall Matrix Product States For Interacting Conformal Field Theories
• ${\mathbb{Z}}_k^{(r)}$-Algebras, FQH Ground States, and Invariants of Binary Forms
• Fermionization, Triangularization and Integrability