Properties of Non-Abelian Fractional Quantum Hall States at Fillingν=k/r

Abstract

We compute the physical properties of non-Abelian Fractional Quantum Hall (FQH) states described by Jack polynomials at general filling ν = 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 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 all non-Abelian states at filling ν = k r .

Gauge Theory, Combinatorics, and Matrix Models

“…This relation pro-vides the explicit interpretation for the partition function of the four dimensional gauge theory as the conformal block of the two dimensional Liouville field theory. It is naturally regarded as a consequence of the M-brane compactifications [5], [6], and also reproduces the results of Seiberg-Witten theory. It shows how Seiberg-Witten curve characterizes the corresponding four dimensional gauge theory, and thus we can obtain a novel viewpoint of Seiberg-Witten theory.…”

Conformal blocks in Virasoro and W theories: Duality and the Calogero–Sutherland model

“…These are the cases of interest for the construction of trial wavefunctions using Jack polynomials in the fractional quantum Hall effect [41,42,43,44]. There the u(1)…”

Universal properties of the FQH state from the topological entanglement entropy and disorder effects

“…It was found [32,33] that the FQH model wavefunctions for RR Z k -parafermion states can be exactly calculated according to Eq. (6) with a negative parameter α and a root 4 configuration (or partition).…”