Boundary states of a bulk gapped ground state in $2$-d quantum spin systems
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929670426984448 |
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| author | Ogata, Yoshiko |
| author_facet | Ogata, Yoshiko |
| contents | We introduce a natural mathematical definition of boundary states of a bulk gapped ground state, in the operator algebraic framework of $2$-d quantum spin systems. With approximate Haag duality at the boundary, we derive a $C^*$-tensor category $\tilde{\mathcal{M}}$ out of such boundary state. Under a non-triviality condition of the braiding in the bulk, we show that the Drinfeld center (with an asymptotic constraint) of $\tilde{\mathcal{M}}$ is equivalent to the bulk braided $C^*$-tensor category derived in [14]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08087 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Boundary states of a bulk gapped ground state in $2$-d quantum spin systems Ogata, Yoshiko Mathematical Physics Statistical Mechanics Operator Algebras We introduce a natural mathematical definition of boundary states of a bulk gapped ground state, in the operator algebraic framework of $2$-d quantum spin systems. With approximate Haag duality at the boundary, we derive a $C^*$-tensor category $\tilde{\mathcal{M}}$ out of such boundary state. Under a non-triviality condition of the braiding in the bulk, we show that the Drinfeld center (with an asymptotic constraint) of $\tilde{\mathcal{M}}$ is equivalent to the bulk braided $C^*$-tensor category derived in [14]. |
| title | Boundary states of a bulk gapped ground state in $2$-d quantum spin systems |
| topic | Mathematical Physics Statistical Mechanics Operator Algebras |
| url | https://arxiv.org/abs/2308.08087 |