Fractional Quantum Hall States and Jack Polynomials

Abstract

We describe an occupation-number-like picture of Fractional Quantum Hall (FQH) states in terms of polynomial wavefunctions characterized by a dominant occupation-number configuration. The bosonic variants of single-component abelian and non-abelian FQH states are modeled by Jacks (Jack symmetric polynomials), characterized by dominant occupation-number configurations satisfying a generalized Pauli principle. In a series of well-known Quantum Hall states, including the Laughlin, Read-Moore, and Read-Rezayi, the Jack polynomials naturally implement a ``squeezing rule'' that constrains allowed configurations to be restricted to those obtained by squeezing the dominant configuration. The Jacks describing uniform FQH states satisfy a highest-weight condition, and a clustering condition which can be generalized to describe quasiparticle states.

4 pages, 2 figures 2 new references added

References in corpus (5)

• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Yang-Baxter equation in spin chains with long range interactions
• A nu=2/5 Paired Wavefunction
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Generalized Quantum Hall Projection Hamiltonians

Cited by in corpus (251)

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• Topological order: from long-range entangled quantum matter to an unification of light and electrons
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• S3 Quantum Hall Wavefunctions
• Jack polynomial fractional quantum Hall states and their generalizations
• Search for exact local Hamiltonians for general fractional quantum Hall states
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
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• Fractional Chern Insulators in Singular Geometries
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• Effective Edge State Dynamics in the Fractional Quantum Hall Effect
• Superconformal minimal models and admissible Jack polynomials
• Analytic Wavefunctions for Neutral Bulk Excitations in Fractional Quantum Hall Fluids
• Multi-Particle Pseudopotentials for Multi-Component Quantum Hall Systems
• Electron-Quasihole Duality and Second Order Differential Equation for Read-Rezayi and Jacks Wavefunctions
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• Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma
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• Extracting higher central charge from a single wave function
• Entanglement Measures for Quasi-Two-Dimensional Fractional Quantum Hall States
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• Success and failure of the plasma analogy for Laughlin states on a torus
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• Bubble phase at $\nu =1/3$ for a spinless hollow-core interaction
• Geometric test for topological states of matter
• Entanglement spectrum edge reconstruction and correlation hole of the FQH liquids
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
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• Reconstruction of Quantum Particle Statistics: Bosons, Fermions, and Transtatistics
• Structure of the nearly-degenerate manifold of lattice quasiholes on a torus
• Thermoelectric Hall conductivity of the fractional quantum Hall systems on a disk
• Determination of many-electron basis functions for a Quantum Hall ground state using Schur polynomials
• Spin-singlet Gaffnian wave function for fractional quantum Hall systems
• The length scale measurements of the Fractional quantum Hall state on cylinder
• Quantum $W_{1+\infty }$ subalgebras of BCD type and symmetric polynomials
• Universal properties of the FQH state from the topological entanglement entropy and disorder effects
• Topological Order in Neural Wavefunctions
• On the geometrical description of fractional Chern insulators based on static structure factor calculations
• Fractional quantum Hall interface induced by geometric singularity
• Edge Induced Topological Phase Transition of the Quantum Hall state at Half Filling
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
• ${\mathbb{Z}}_k^{(r)}$-Algebras, FQH Ground States, and Invariants of Binary Forms
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
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• Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions
• Particle Propagator of Spin Calogero-Sutherland Model
• Refermionized theory of the edge modes of a fractional quantum Hall cloud
• Transitions from Composite Fermi Liquid to Moore-Read States in Weyl Semimetals
• Computing nonsymmetric and interpolation Macdonald polynomials
• Fermionization, Triangularization and Integrability
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• Jack on a Devil's staircase
• Almost linear Haldane pseudopotentials and emergent conformal block wave-functions in a Landau level
• Boundary critical phenomena in the quantum Ashkin-Teller model
• Disordered statistical physics in low dimensions: extremes, glass transition, and localization
• Jack polynomials with prescribed symmetry and some of their clustering properties
• Search for electron liquids with non-Abelian quasiparticles
• Complexity of the Laughlin wave function from the Dyson-orbital perspective