SU(m) non-Abelian anyons in the Jain hierarchy of quantum Hall states

TL;DR

This paper demonstrates that the Jain hierarchy of fractional quantum Hall states hosts non-Abelian SU(m) anyons, distinguished by their edge excitation algebra, with implications for topological quantum computing.

Contribution

It identifies the realization of fundamental topological order in Jain states via the $W_{1+ obreak 1+ obreak ext{infinity}}$ algebra and proposes experimental detection through topological entanglement entropy.

Findings

Jain hierarchy states exhibit non-Abelian SU(m) anyons.

These states have lower entanglement entropy than Abelian states.

Potential use of non-Abelian anyons for topological quantum computation.

Abstract

We show that different classes of topological order can be distinguished by the dynamical symmetry algebra of edge excitations. Fundamental topological order is realized when this algebra is the largest possible, the algebra of quantum area-preserving diffeomorphisms, called $W_{1+\infty}$. We argue that this order is realized in the Jain hierarchy of fractional quantum Hall states and show that it is more robust than the standard Abelian Chern-Simons order since it has a lower entanglement entropy due to the non-Abelian character of the quasi-particle anyon excitations. These behave as SU($m$) quarks, where $m$ is the number of components in the hierarchy. We propose the topological entanglement entropy as the experimental measure to detect the existence of these quantum Hall quarks. Non-Abelian anyons in the $\nu = 2/5$ fractional quantum Hall states could be the primary candidates to realize qbits for topological quantum computation.