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

In summary, "symmetry protected topological phases" refer to gapped phases of matter that preserve certain symmetries, such as time reversal or spatial symmetry. These phases have unique ground states on closed surfaces, but show nontrivial edge modes on open surfaces. This term is often encountered in discussions of topological phases of matter.
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physics2023
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What is meant when a phase is said to have "symmetry protected"?
What is meant when a phase is said to have "symmetry protected"?
 
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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.
 
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Nugatory said:
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"
 
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physics2023 said:
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.
 
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physics2023 said:
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.
 
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DrClaude said:
You have a full document explaining what you are asking???
I guess he wants a simpler explanation than given in the paper.
 

1. What does it mean for a phase to have "symmetry protection"?

When a phase is said to have "symmetry protection", it means that there is a fundamental symmetry present in the system that prevents the phase from undergoing a phase transition. In other words, the symmetry acts as a barrier that protects the phase from changing into a different phase.

2. How does symmetry protection affect the properties of a phase?

Symmetry protection can greatly influence the properties of a phase. It can lead to the emergence of new physical phenomena, such as topological order, and can also enhance the stability of the phase by preventing it from undergoing a phase transition.

3. What types of symmetries can protect a phase?

There are various types of symmetries that can protect a phase, including spatial symmetries (such as translation, rotation, and reflection symmetries), time-reversal symmetry, and internal symmetries (such as gauge symmetries). These symmetries can act individually or in combination to protect a phase.

4. Can symmetries be broken in a phase with symmetry protection?

No, symmetries cannot be broken in a phase with symmetry protection. This is because the symmetry acts as a fundamental constraint that prevents the phase from undergoing a phase transition, which would result in a broken symmetry.

5. How is the concept of symmetry protection relevant in the study of condensed matter physics?

The concept of symmetry protection is highly relevant in the study of condensed matter physics. It helps in understanding the properties of different phases and in predicting the behavior of materials under different conditions. It is also crucial in the development of new materials with desired properties, such as topological insulators, which rely on symmetry protection for their unique properties.

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