I am trying to understand the symmetry protected topological phase. Most papers only explain the symmetry but none of them explain the meaning of "topological". My question is : What's the meaning of "topological" in "symmetry protected topological phase"?
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2$\begingroup$ Perhaps this can (partially) answer your question: physics.stackexchange.com/questions/57179/…. I can provide additional details if necessary. $\endgroup$– NanoPhysCommented Sep 19, 2013 at 18:45
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The follow article directly address your question (which is a very good question):
Reconciling topological insulators and topological order
The article explains the different meaning of "topological" in "topological insulators" and "topological order".
answered Oct 6, 2013 at 14:48