Domain walls, fusion rules and conformal field theory in the quantum Hall regime

Abstract

We provide a simple way to obtain the fusion rules associated with elementary quasi-holes over quantum Hall wave functions, in terms of domain walls. The knowledge of the fusion rules is helpful in the identification of the underlying conformal field theory describing the wave functions. We obtain the fusion rules, and explicitly give a conformal field theory description, for a two-parameter family (k,r) of wave functions. These include the Laughlin, Moore-Read and Read-Rezayi states when r=2. The `gaffnian' wave function is the prototypical example for r>2, in which case the conformal field theory is non-unitary.

4 pages

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Cited by in corpus (8)

• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Conformal invariance of chiral edge theories
• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Gaplessness of the Gaffnian
• Spin chain description of rotating bosons at $\nu =1$
• Transition from two-component 332 Halperin state to one-component Jain state at filling factor ν=2/5
• Conformal field theory construction for nonabelian hierarchy wave functions