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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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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".

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