Topological order from quantum loops and nets

Understand

I define models of quantum loops and nets which have ground states with topological order.

• These make possible excited states comprised of deconfined anyons with non-abelian braiding.
• With the appropriate inner product, these quantum loop models are equivalent to net models whose topological weight involves the chromatic polynomial.
• A useful consequence is that the models have a quantum self-duality, making it possible to find a simple Hamiltonian preserving the topological order.