The Essence of Emergent Origins H: A Functorial Interpretation Framework Based on Category Theory for the Unified Criteria of Topological Order Emergence
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2025
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| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17844355 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | The Essence of Emergent Origins H: A Functorial Interpretation Framework Based on Category Theory for the Unified Criteria of Topological Order Emergence zhou, changzheng zhou, ziqing Topological order; Emergence criteria; Category theory; Topological quantum field theory; Unitary fusion category; Quantum information <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> |
| title | The Essence of Emergent Origins H: A Functorial Interpretation Framework Based on Category Theory for the Unified Criteria of Topological Order Emergence |
| topic | Topological order; Emergence criteria; Category theory; Topological quantum field theory; Unitary fusion category; Quantum information |
| url | https://doi.org/10.5281/zenodo.17844355 |