Tensor category describing anyons in the quantum Hall effect and quantization of conductance
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913813335375872 |
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| author | Bachmann, Sven Corbelli, Matthew Fraas, Martin Ogata, Yoshiko |
| author_facet | Bachmann, Sven Corbelli, Matthew Fraas, Martin Ogata, Yoshiko |
| contents | In this study, we examine the quantization of Hall conductance in an infinite plane geometry. We consider a microscopic charge-conserving system with a pure, gapped infinite-volume ground state. While Hall conductance is well-defined in this scenario, existing proofs of its quantization have relied on assumptions of either weak interactions, or properties of finite volume ground state spaces, or invertibility. Here, we assume that the conditions necessary to construct the braided $C^*$-tensor category which describes anyonic excitations are satisfied, and we demonstrate that the Hall conductance is rational if the tensor category is finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor category describing anyons in the quantum Hall effect and quantization of conductance Bachmann, Sven Corbelli, Matthew Fraas, Martin Ogata, Yoshiko Mathematical Physics Quantum Physics 81R15, 81T40 In this study, we examine the quantization of Hall conductance in an infinite plane geometry. We consider a microscopic charge-conserving system with a pure, gapped infinite-volume ground state. While Hall conductance is well-defined in this scenario, existing proofs of its quantization have relied on assumptions of either weak interactions, or properties of finite volume ground state spaces, or invertibility. Here, we assume that the conditions necessary to construct the braided $C^*$-tensor category which describes anyonic excitations are satisfied, and we demonstrate that the Hall conductance is rational if the tensor category is finite. |
| title | Tensor category describing anyons in the quantum Hall effect and quantization of conductance |
| topic | Mathematical Physics Quantum Physics 81R15, 81T40 |
| url | https://arxiv.org/abs/2410.04736 |