1209.6040 (Belén Paredes)

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

Belén Paredes

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.

View original: http://arxiv.org/abs/1209.6040