Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry

Abstract

We show that a large class of bosonic spin-singlet Fractional Quantum Hall model wave-functions and their quasi-hole excitations can be written in terms of Jack polynomials with a prescribed symmetry. Our approach describes new spin-singlet quantum Hall states at filling fraction nu = 2k/(2r-1) and generalizes the (k,r) spin-polarized Jack polynomial states. The NASS and Halperin spin singlet states emerge as specific cases of our construction. The polynomials express many-body states which contain configurations obtained from a root partition through a generalized squeezing procedure involving spin and orbital degrees of freedom. The corresponding generalized Pauli principle for root partitions is obtained, allowing for counting of the quasihole states. We also extract the central charge and quasihole scaling dimension, and propose a conjecture for the underlying CFT of the (k, r) spin-singlet Jack states.

17 pages, 1 figure

References in corpus (9)

• Fractional Quantum Hall States and Jack Polynomials
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Conformal invariance of chiral edge theories
• Wavefunctions for topological quantum registers
• On polynomials interpolating between the stationary state of a O(n) model and a Q.H.E. ground state
• Central Charge and Quasihole Scaling Dimensions From Model Wavefunctions: Towards Relating Jack Wavefunctions to W-algebras
• Symmetric polynomials vanishing on the shifted diagonals and Macdonald polynomials
• Quasiparticle spin from adiabatic transport in quantum Hall trial wavefunctions

Cited by in corpus (21)

• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Quantum Hall Effect of Two-Component Bosons at Fractional and Integral Fillings
• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Non-Abelian spin singlet states of two-component Bose gases in artificial gauge fields
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Multi-Particle Pseudopotentials for Multi-Component Quantum Hall Systems
• Topological d-wave pairing structures in Jain states
• Quantum Hall Edges with Hard Confinement: Exact Solution beyond Luttinger Liquid
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• Exact closed-form analytic wave functions in two dimensions: Contact-interacting fermionic spinful ultracold atoms in a rapidly rotating trap
• Spinless basis for spin-singlet FQH states
• Virasoro Constraint for Uglov Matrix Model
• Spin-singlet Gaffnian wave function for fractional quantum Hall systems
• Disordered statistical physics in low dimensions: extremes, glass transition, and localization