String-net condensation: A physical mechanism for topological phases

@article{Levin2005StringnetCA,
  title={String-net condensation: A physical mechanism for topological phases},
  author={Michael Levin and Xiao-Gang Wen},
  journal={Physical Review B},
  year={2005},
  volume={71},
  pages={045110}
}
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,'' become highly fluctuating and condense. We construct a large class of exactly soluble 2D spin Hamiltonians whose ground states are string-net condensed. Each ground state corresponds to a different parity invariant topological phase. The models reveal the mathematical framework underlying topological… 
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