Exploring topological entanglement through Dehn surgery
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913231424978944 |
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| author | Dwivedi, Aditya Dwivedi, Siddharth Singh, Vivek Kumar Ramadevi, Pichai Mandal, Bhabani Prasad |
| author_facet | Dwivedi, Aditya Dwivedi, Siddharth Singh, Vivek Kumar Ramadevi, Pichai Mandal, Bhabani Prasad |
| contents | We compute the $\text{PSL}(2,\mathbb{C})$ Chern-Simons partition function of a closed 3-manifold obtained from Dehn fillings of the link complement $\mathbf S^3\backslash {\mathcal{L}}$, where $\mathcal{L}=\mathcal{K}# H$ is the connected sum of the knot $\mathcal {K}$ with the Hopf link $H$. Motivated by our earlier work on topological entanglement and the reduced density matrix $σ$ for such link complements, we wanted to determine a choice of Dehn filling so that the trace of the matrix $σ$ becomes equal to the $\text{PSL}(2,\mathbb{C})$ partition function of the closed 3-manifold. We use the SnapPy program and numerical techniques to show this equivalence up to the leading order. We have given explicit results for all hyperbolic knots $\mathcal{K}$ up to six crossings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploring topological entanglement through Dehn surgery Dwivedi, Aditya Dwivedi, Siddharth Singh, Vivek Kumar Ramadevi, Pichai Mandal, Bhabani Prasad High Energy Physics - Theory Mathematical Physics Quantum Physics We compute the $\text{PSL}(2,\mathbb{C})$ Chern-Simons partition function of a closed 3-manifold obtained from Dehn fillings of the link complement $\mathbf S^3\backslash {\mathcal{L}}$, where $\mathcal{L}=\mathcal{K}# H$ is the connected sum of the knot $\mathcal {K}$ with the Hopf link $H$. Motivated by our earlier work on topological entanglement and the reduced density matrix $σ$ for such link complements, we wanted to determine a choice of Dehn filling so that the trace of the matrix $σ$ becomes equal to the $\text{PSL}(2,\mathbb{C})$ partition function of the closed 3-manifold. We use the SnapPy program and numerical techniques to show this equivalence up to the leading order. We have given explicit results for all hyperbolic knots $\mathcal{K}$ up to six crossings. |
| title | Exploring topological entanglement through Dehn surgery |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2402.07459 |