Merging Quantum Loop Gases: a Route to Non-Abelian Topological Phases

TL;DR

This paper proposes a method to generate non-Abelian topological phases by merging Abelian quantum loop condensates, specifically using a symmetrization process on two toric-code models, resulting in non-Abelian excitations with potential quantum computing applications.

Contribution

It introduces a novel merging technique of Abelian quantum loop gases to realize non-Abelian topological phases, with an explicit spin-1 Hamiltonian model demonstrating the concept.

Findings

Merging two toric-code quantum loop gases yields non-Abelian excitations.

The constructed Hamiltonian has a unique gapped ground state.

Excitations exhibit non-Abelian braiding properties.

Abstract

Condensation of quantum loops naturally leads to topological phases with Abelian excitations. Here, I propose that non-Abelian topological phases can arise from merging two (or several) identical Abelian quantum loop condensates. I define merging through a symmetrization operation, which makes the two loop condensates indistinguishable, inducing the possibility of a topological degeneracy in the space of quasiparticles. To illustrate the construction, the case of two identical toric-code quantum loop gases is considered. A spin-1 model for the two dimensional square lattice is presented for which the resulting merged state is the exact unique ground state. This Hamiltonian involves four-body interactions between spins located at the same plaquette or vertex, which are quadratic in the spin-1 operators. Vertex and plaquette interaction terms are not mutually commuting. The model displays gapped excitations which result from merging anyons in both toric-code copies. These excitations exhibit non-Abelian braiding properties.