What is meant when a phase is said to have "symmetry protected"?

[physics2023]

TL;DR Summary

What is meant when a phase is said to have "symmetry protected"?

What is meant when a phase is said to have "symmetry protected"?

 

[Nugatory]

You will get better and more helpful answers if you tell us where you encountered that term. Without that information we’re just going to be guessing what the unknown author meant.

 

[physics2023]

You will get better and more helpful answers if you tell us where you encountered that term. Without that information we’re just going to be guessing what the unknown author meant.

I recently encountered the topic of topological phases of matter. There I encountered the following term:
"symmetry protected topological phases"

 

[PeterDonis]

I recently encountered the topic of topological phases of matter. There I encountered the following term:
"symmetry protected topological phases"

Where did you encounter these things? We need a specific reference--book, article, paper, website, etc.--not just a description of what you found.

 

[physics2023]

Where did you encounter these things? We need a specific reference--book, article, paper, website, etc.--not just a description of what you found.

https://www.its.caltech.edu/~xcchen/img/Summer_School/lecture-CalSWARM.pdf

 

[DrClaude]

https://www.its.caltech.edu/~xcchen/img/Summer_School/lecture-CalSWARM.pdf

You have a full document explaining what you are asking???

Symmetry protected topological phases are gapped phases with certain global symmetry (time reversal, charge conjugation, discrete $Z_N$ symmetry, spatial symmetry etc.). The ground state does not spontaneously break the symmetry and is unique on closed manifolds. On an open manifold on the other hand, the system has nontrivial edge modes (degenerate or gapless) such that there cannot be a unique gapped ground state.

 

[Demystifier]

You have a full document explaining what you are asking???

I guess he wants a simpler explanation than given in the paper.