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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 7th 2020

added these pointers on classification of topological phases of matter via tensor network states:

• C. Wille, O. Buerschaper, Jens Eisert, Fermionic topological quantum states as tensor networks, Phys. Rev. B 95, 245127 (2017) (arXiv:1609.02574)

• Andreas Bauer, Jens Eisert, Carolin Wille, Towards a mathematical formalism for classifying phases of matter (arXiv:1903.05413)

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeFeb 12th 2021

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 14th 2021

• Sanju Gupta, Avadh Saxena, The Role of Topology in Materials, Springer Series in Solid-State Sciences 189, 2018 (doi:10.1007/978-3-319-76596-9)
• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMay 19th 2021

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMay 6th 2022

The Idea-section of this entry was no good, besides being extremely brief. I have now written a few paragraphs (here). Still much room to improve on this, but it should be a start.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMay 6th 2022

• Online course on topology in condensed matter (2015-) $[$topocondmat.org$]$
• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeMay 6th 2022

I have renamed the entry from “topological state of matter” to “topological phase of matter”. The latter is the established terminology, and the former doesn’t really make sense.

• CommentRowNumber8.
• CommentAuthorDavid_Corfield
• CommentTimeMay 10th 2022

In that introductory paragraph

… if external adiabatic deformations of the system that are gentle enough not to excite modes beyond energy >Δ above the ground state leave the properties of the system invariant if the deformations are small…

the final “if the deformations are small” is a repetition? The whole paragraph being a single sentence it’s hard to parse.

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMay 10th 2022

Right, thanks for pushing me. I have now adjusted and then I have expanded the idea-section a fair bit more (still here)

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMay 10th 2022

added also a paragraph (now here) making the relation to TQFT more explicit

• CommentRowNumber11.
• CommentAuthorDavid_Corfield
• CommentTimeMay 11th 2022

Thanks! That’s much clearer.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeMay 14th 2022

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTime12 hours ago