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

TL;DR

This paper demonstrates that a broad class of bosonic spin-singlet Fractional Quantum Hall wave-functions and their excitations can be represented using Jack polynomials with specific symmetries, generalizing previous models and connecting to conformal field theory.

Contribution

It introduces a new framework expressing spin-singlet quantum Hall states via Jack polynomials with prescribed symmetry, extending known models and providing tools for state counting and CFT connections.

Findings

Representation of spin-singlet states with Jack polynomials

Generalized squeezing procedure for configurations

Conjecture relating states to underlying CFT

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.