Mixed state topological order: operator algebraic approach
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917884144386048 |
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| author | Ogata, Yoshiko |
| author_facet | Ogata, Yoshiko |
| contents | We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided $C^*$-tensor category to each state satisfying a mixed-state version of the approximate Haag duality. We study how this category behaves under decoherence: suppose the state is acted by a finite depth quantum channel. We prove that the braided $C^*$-tensor category of the final state is a braided $C^*$-tensor subcategory of the initial state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02398 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed state topological order: operator algebraic approach Ogata, Yoshiko Mathematical Physics Statistical Mechanics Quantum Physics We study the classification problem of mixed states in two-dimensional quantum spin systems in the operator algebraic framework of quantum statistical mechanics. We associate a braided $C^*$-tensor category to each state satisfying a mixed-state version of the approximate Haag duality. We study how this category behaves under decoherence: suppose the state is acted by a finite depth quantum channel. We prove that the braided $C^*$-tensor category of the final state is a braided $C^*$-tensor subcategory of the initial state. |
| title | Mixed state topological order: operator algebraic approach |
| topic | Mathematical Physics Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2501.02398 |