Fractional Quantum Hall States and Jack Polynomials

Abstract

We describe an occupation-number-like picture of Fractional Quantum Hall (FQH) states in terms of polynomial wavefunctions characterized by a dominant occupation-number configuration. The bosonic variants of single-component abelian and non-abelian FQH states are modeled by Jacks (Jack symmetric polynomials), characterized by dominant occupation-number configurations satisfying a generalized Pauli principle. In a series of well-known Quantum Hall states, including the Laughlin, Read-Moore, and Read-Rezayi, the Jack polynomials naturally implement a ``squeezing rule'' that constrains allowed configurations to be restricted to those obtained by squeezing the dominant configuration. The Jacks describing uniform FQH states satisfy a highest-weight condition, and a clustering condition which can be generalized to describe quasiparticle states.

4 pages, 2 figures 2 new references added

References in corpus (1)

• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$

Cited by in corpus (10)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• 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 properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems
• Fractional quantum Hall state at ν=1/4 in a wide quantum well
• 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
• Spin chain description of rotating bosons at $\nu =1$