Topological order from quantum loops and nets

Details Topological order from quantum loops and nets Topological order from quantum loops and nets

2008-04-03

arxiv.org/abs/0804.0625v2

Annals of Physics 323 (2008) 3113

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1016/j.aop.2008.04.011

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.

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