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

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

2008-03-19

arxiv.org/abs/0803.2882v1

Phys. Rev. Lett. 101, 246806 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

2 figures

Scientific paper

10.1103/PhysRevLett.101.246806

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 $\nu=\frac{k}{r}$.

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