Topological order from quantum loops and nets Original Research Article

I define models of quantum loops and nets that 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 simple Hamiltonian preserving the topological order is found by exploiting quantum self-duality. For the square lattice, this Hamiltonian has only four-spin interactions.