Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu=\frac{k}{r}$

TL;DR

This paper analyzes the physical properties of non-Abelian fractional quantum Hall states described by Jack polynomials at various filling fractions, revealing new states and their connection to conformal field theories.

Contribution

It introduces a comprehensive computation of physical properties for Jack polynomial-based non-Abelian FQH states at general filling fractions, including new states for r>2.

Findings

Identifies new non-Abelian FQH states for r>2.

Calculates thermal Hall coefficient, quantum dimensions, and quasihole propagator.

Shows the quasihole wavefunction structure is identical across all such states.

Abstract

We compute the physical properties of non-Abelian Fractional Quantum Hall (FQH) states described by Jack polynomials at general filling $\nu=\frac{k}{r}$. For $r=2$, these states are identical to the $Z_k$ Read-Rezayi parafermions, whereas for $r>2$ they represent new FQH states. The $r=k+1$ states, multiplied by a Vandermonde determinant, are a non-Abelian alternative construction of states at fermionic filling $2/5, 3/7, 4/9...$. We obtain the thermal Hall coefficient, the quantum dimensions, the electron scaling exponent, and show that the non-Abelian quasihole has a well-defined propagator falling off with the distance. The clustering properties of the Jack polynomials, provide a strong indication that the states with $r>2$ can be obtained as correlators of fields of \emph{non-unitary} conformal field theories, but the CFT-FQH connection fails when invoked to compute physical properties such as thermal Hall coefficient or, more importantly, the quasihole propagator. The quasihole wavefuntion, when written as a coherent state representation of Jack polynomials, has an identical structure for \emph{all} non-Abelian states at filling $\nu=\frac{k}{r}$.