Mechanism of Topological Order
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A large class of topological orders is realized through a mechanism called string-net condensation. This class of topological orders can be classified by utilizing tensor category (or monoidal category) theory. One finds that string-net condensation can generate infinitely many different types of topological orders, which may indicate that there are many different new types of materials remaining to be discovered.
The collective motions of condensed strings give rise to excitations above the string-net condensed states. Those excitations turn out to be gauge bosons. The ends of strings are defects which correspond to another type of excitations. Those excitations are the gauge charges and can carry Fermi or fractional statistics.
The condensations of other extended objects such as "membranes", "brane-nets", and fractals also lead to topologically ordered phases and "quantum glassiness".
Read more about this topic: Topological Order
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