From Irrational to Non-Unitary: on the Haffnian and Haldane-Rezayi wave functions

Abstract

We study the Haffnian and Haldane-Rezayi quantum Hall wave functions and their quasihole excitations by means of their `root configurations', and point out a close connection between these seemingly different states. For both states, we formulate a `generalized Pauli-principle', which allows to count the degeneracies of these states. The connection between these states might elucidate the underlying theory describing the `irrational' Haffnian state.

4+ pages, published version

References in corpus (6)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Fractional Quantum Hall States and Jack Polynomials
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• One-Dimensional Theory of the Quantum Hall System
• Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
• A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states

Cited by in corpus (7)

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• The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect
• Fractionalisation and dynamics of anyons at $\nu =n+1/3$ in fractional quantum Hall effect and their experimental signatures
• Two-component parton fractional quantum Hall state in graphene
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• ${\mathbb{Z}}_k^{(r)}$-Algebras, FQH Ground States, and Invariants of Binary Forms
• Non-quasiconvex dispersion of composite fermions and the fermionic Haffnian state in the first-excited Landau level