A general approach to quantum Hall hierarchies

Abstract

The abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states emanating from the ν = 5/2 Moore-Read state in the second Landau level. Extending a recently developed formalism for hierarchical quasihole condensation, we present a theory that allows for the explicit construction of the ground state wave function, as well as its quasiparticle excitations, for any state based on the abelian hierarchy. We relate our construction to structures in rational conformal field theory and stress the importance of using coherent state wave functions which allows us to formulate an extension of the bulk - edge correspondence that was conjectured by Moore and Read. Finally, we study the proposed ground state wave functions in the limiting geometry of a thin torus and argue that they coincide with the known exact results.

18 pages

References in corpus (16)

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• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
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Cited by in corpus (16)

• Quantum Hall Physics - hierarchies and CFT techniques
• Hall Viscosity of Hierarchical Quantum Hall States
• Composite Fermions on a Torus
• Condensate-induced transitions and critical spin chains
• Focus on topological quantum computation
• Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
• The quantum Hall hierarchy in spherical geometry
• Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models
• Coherent State Wave Functions on a Torus with a Constant Magnetic Field
• Energy projection and modified Laughlin states
• Matrix product state representation of quasielectron wave functions
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Composite Fermion Wavefunctions Derived by Conformal Field Theory
• Continuum limit of lattice quasielectron wavefunctions
• Generalization of Laughlin's Theory for the Fractional Quantum Hall Effect
• Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states