Microscopic theory of the quantum Hall hierarchy

Abstract

We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan {\it et. al.}, and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states.

4 pages, 2 figures. Published

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• Quantum Hall quasielectron operators in conformal field theory
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• Hall Viscosity of Hierarchical Quantum Hall States
• Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations
• Quantum Hall quasielectrons - Abelian and non-Abelian
• Quantum Hall wave functions on the torus
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• Hierarchy wave functions--from conformal correlators to Tao-Thouless states
• Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
• Vortex-hole duality: a unified picture of weak and strong-coupling regimes of bosonic ladders with flux
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• Solvable models for unitary and non-unitary topological phases
• Anisotropic Pseudopotential Characterization of Quantum Hall Systems under Tilted Magnetic Field
• Devil's staircases in synthetic dimensions and gauge fields
• Devil's staircase phase diagram of the fractional quantum Hall effect in the thin-torus limit
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• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• The quantum Hall hierarchy in spherical geometry
• A general approach to quantum Hall hierarchies
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• S3 Quantum Hall Wavefunctions
• Multi-Particle Pseudopotentials for Multi-Component Quantum Hall Systems
• Effective spin chains for fractional quantum Hall states
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• Laughlin states and their quasi-particle excitations on the torus
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• Edge properties of principal fractional quantum Hall states in the cylinder geometry
• Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains
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• Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation
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• Gaffnian holonomy through the coherent state method
• Generalized Devil's staircase and RG flows
• Unified Fock space representation of fractional quantum Hall states
• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
• Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view
• Exclusion statistics for quantum Hall states in Tao-Thouless limit
• Composite Fermion Wavefunctions Derived by Conformal Field Theory
• Lifshitz tails at spectral edge and holography with a finite cutoff
• Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states
• Strange Metal to Insulator Transitions in the Lowest Landau Level
• Current quantization and fractal hierarchy in a driven repulsive lattice gas
• A simple view on the quantum Hall system
• Hierarchy Construction of Quantum Hall States and Non-Commutative Chern-Simons Theory