Topological order from quantum loops and nets

Abstract

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. For the square lattice, this Hamiltonian has only four-spin interactions.

References in corpus (4)

• Non-Abelian Anyons and Topological Quantum Computation
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
• An extended Hubbard model with ring exchange: a route to a non-Abelian topological phase
• Local interactions and non-Abelian quantum loop gases

Cited by in corpus (7)

• Condensate induced transitions between topologically ordered phases
• Universal entanglement entropy in 2D conformal quantum critical points
• Exact entanglement renormalization for string-net models
• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Non-Abelian statistics as a Berry phase in exactly solvable models
• Local interactions and non-Abelian quantum loop gases