Non-Abelian Topological Order from Quantum Organization in Indistinguishable Groups

TL;DR

This paper introduces a framework where non-Abelian topological order emerges from symmetrizing identical quantum many-body states, demonstrated through a symmetrized toric code model exhibiting non-Abelian quasiparticles.

Contribution

It presents a novel method to generate non-Abelian topological models from Abelian ones via quantum symmetrization, linking entanglement and topological degeneracy.

Findings

Symmetrization leads to non-Abelian braiding statistics.

The symmetrized toric code model exhibits non-Abelian quasiparticles.

Entanglement properties reveal non-Abelian hidden order.

Abstract

I propose that non-Abelian topological order can emerge from the organization of quantum particles into identical indistinguishable copies of the same quantum many-body state. Quantum indistinguishability (symmetrization) of the collectivities leads to topological degeneracy in the subspace of elementary excitations, giving rise to non-Abelian braiding statistics. The non-Abelian hidden order of a symmetrized structure is manifested in its entanglement properties, and the corresponding non-Abelian fusion and braiding rules can be derived by analyzing the set of symmetrized states on a surface with non-trivial topology like a torus. To illustrate the emergence of non-Abelian statistics from symmetrization, I consider the case of two identical copies of the toric code model. The resulting model is shown to be non-Abelian, exhibiting two types (charge and flux) of quasiparticles with non trivial fusion channels. The symmetrization construction I present here constitutes a framework for the generation of non-Abelian models from known Abelian ones.