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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"?
I recently encountered the topic of topological phases of matter. There I encountered the following term: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.
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 said:I recently encountered the topic of topological phases of matter. There I encountered the following term:
"symmetry protected topological phases"
https://www.its.caltech.edu/~xcchen/img/Summer_School/lecture-CalSWARM.pdfPeterDonis said:Where did you encounter these things? We need a specific reference--book, article, paper, website, etc.--not just a description of what you found.
You have a full document explaining what you are asking???physics2023 said:
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.
I guess he wants a simpler explanation than given in the paper.DrClaude said:You have a full document explaining what you are asking???
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.
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.
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.
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.
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.