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| Main Authors: | , |
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| Format: | Recurso digital |
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Zenodo
2025
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| Subjects: | |
| Online Access: | https://doi.org/10.5281/zenodo.17844355 |
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Table of Contents:
- <p>The diagnosis of topological order emergence relies on three phenomenological<br>criteria: structural stability (S), information efficiency (E), and dynamical accessi<br>bility (D). However, their underlying unified mathematical foundation has not yet<br>been clarified. This paper proposes a functorial interpretation framework based on<br>category theory and topological quantum field theory (TQFT), demonstrating that<br>S, E, D can be regarded as natural derived quantities of the unitary fusion category<br>(UFC) describing the system’s topological order, or equivalently, of the correspond<br>ing (2+1)-dimensional TQFT functor, in different physical contexts. This ”single<br>functor, multiple sections” picture not only provides a self-consistent mathemati<br>cal foundation for the three criteria, bridging the gap between physical intuition<br>and mathematical rigor, but also naturally explains the interrelations among the<br>criteria. This framework provides a deeper theoretical perspective for the system<br>atic classification, resource assessment, and experimental detection of topological<br>orders.</p>