Nested Topological Order

TL;DR

This paper introduces nested topological order in quantum lattice models with non-abelian gauge symmetry, exploring how symmetry reduction affects topological degeneracy and extends quantum computation capabilities.

Contribution

It presents the concept of nested topological order and analyzes how gauge symmetry reduction influences topological properties and quantum computational potential.

Findings

Symmetry reduction creates boundary conditions affecting topological degeneracy.

Topological fluxes and hidden charges relate to ground state degeneracy.

Island deformations extend topological quantum computation beyond quasiparticles.

Abstract

We introduce the concept of nested topological order in a class of exact quantum lattice Hamiltonian models with non-abelian discrete gauge symmetry. The topological order present in the models can be partially destroyed by introducing a gauge symmetry reduction mechanism. When symmetry is reduced in several islands only, this imposes boundary conditions to the rest of the system giving rise to topological ground state degeneracy. This degeneracy is related to the existence of topological fluxes in between islands or, alternatively, hidden charges at islands. Additionally, island deformations give rise to an extension of topological quantum computation beyond quasiparticles.