Bridge between Abelian and Non-Abelian Fractional Quantum Hall States

Abstract

We propose a scheme to construct the most prominent Abelian and non-Abelian fractional quantum Hall states from K-component Halperin wave functions. In order to account for a one-component quantum Hall system, these SU(K) colors are distributed over all particles by an appropriate symmetrization. Numerical calculations corroborate the picture that the proposed scheme allows for a unification of both Abelian and non-Abelian trial wave functions in the study of one-component quantum Hall systems.

4 pages, 2 figures; revised version, published in Phys. Rev. Lett

References in corpus (13)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
• Parafermion Hall states from coset projections of abelian conformal theories
• A nu=2/5 Paired Wavefunction
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets
• Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
• Non-Abelian states with negative flux: a new series of quantum Hall states
• The plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries
• Wavefunctions and counting formulas for quasiholes of clustered quantum Hall states on a sphere
• Parafermion statistics and the application to non-abelian quantum Hall states

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• Decomposition of fractional quantum Hall states: New symmetries and approximations
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• Tunneling-driven breakdown of the 331 state and the emergent Pfaffian and composite Fermi liquid phases
• Fractional quantum Hall state at ν=1/4 in a wide quantum well
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• The structure of spinful quantum Hall states: a squeezing perspective
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• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• A Matrix Model for Non-Abelian Quantum Hall States
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• Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• S3 Quantum Hall Wavefunctions
• Nonperturbative approach to the quantum Hall bilayer
• Gaplessness of the Gaffnian
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system
• Topological d-wave pairing structures in Jain states
• Hamiltonian theory for Quantum Hall systems in a tilted magnetic field: robustness of activation gaps
• Gaffnian holonomy through the coherent state method
• Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect
• Phase diagram of $\nu =\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings
• Properties of 2D anyon gas
• Transition from two-component 332 Halperin state to one-component Jain state at filling factor ν=2/5
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
• Spin-singlet Gaffnian wave function for fractional quantum Hall systems
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Non-Abelian phases from the condensation of Abelian anyons