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I'm looking for a pedagogical review or book about topological phases, topological order, TQFTs, and related subjects.

The ideal thing would be a mix of rigorous definitions and physical examples, with something giving me a physical idea of what's going on.

Right now the only things I can find are either a lot of category theory with no physics at all or a lot of handwaving about the Toric code (after having read about it in a bunch of different sources, I still don't understand what's "topological" about it, or how does it exemplify a more general concept of "topological order").

Does anybody know anything of the sort?

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  • $\begingroup$ A potentially interesting book is the upcoming "Topological Phases of Matter" by R. Moessner and J.E. Moore. Posting it as a comment instead of an answer, because I haven't read it, and can't really comment on how well it fits your criteria. $\endgroup$
    – Anyon
    May 3, 2021 at 13:16

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For topological band theory (single-particle picture) the online course by TU Delft could be a nice starting point. A more thorough approach on topological insulators can be found at the lecture notes by Aboth or at the classic book Topological Insulators and Topological Superconductors by A. Bernevig for instance.

On topological order, TQFTs and the toric code, S. Simon has a nice protobook at his website.

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