On the structure of DHR bimodules of abstract spin chains
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909817184976896 |
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| author | Hataishi, Lucas Jaklitsch, David Jones, Corey Yamashita, Makoto |
| author_facet | Hataishi, Lucas Jaklitsch, David Jones, Corey Yamashita, Makoto |
| contents | Abstract spin chains axiomatize the structure of local observables on the 1D lattice which are invariant under a global symmetry, and arise at the physical boundary of 2+1D topologically ordered spin systems. In this paper, we study tensor categorical properties of DHR bimodules over abstract spin chains. Assuming that the charge transporters generate the algebra of observables, we prove that the associated category has a structure of modular tensor category with respect to the natural braiding. Under an additional assumption of algebraic Haag duality, this category becomes the Drinfeld center of the half-line fusion category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the structure of DHR bimodules of abstract spin chains Hataishi, Lucas Jaklitsch, David Jones, Corey Yamashita, Makoto Quantum Algebra Mathematical Physics Operator Algebras Abstract spin chains axiomatize the structure of local observables on the 1D lattice which are invariant under a global symmetry, and arise at the physical boundary of 2+1D topologically ordered spin systems. In this paper, we study tensor categorical properties of DHR bimodules over abstract spin chains. Assuming that the charge transporters generate the algebra of observables, we prove that the associated category has a structure of modular tensor category with respect to the natural braiding. Under an additional assumption of algebraic Haag duality, this category becomes the Drinfeld center of the half-line fusion category. |
| title | On the structure of DHR bimodules of abstract spin chains |
| topic | Quantum Algebra Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2504.06094 |