Bulk-boundary correspondence from hyper-invariant tensor networks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908179788464128 |
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| author | Bistroń, Rafał Hontarenko, Mykhailo Życzkowski, Karol |
| author_facet | Bistroń, Rafał Hontarenko, Mykhailo Życzkowski, Karol |
| contents | We introduce a tensor network designed to faithfully simulate the AdS/CFT correspondence, akin to the multi-scale entanglement renormalization ansatz (MERA), following hyper-invariant tensor network. The proposed construction integrates bulk indices within the network architecture to uphold the key features of the HaPPY code, including complementary recovery. This framework accurately reproduces the boundary conformal field theory's (CFT) two- and three-point correlation functions, while considering the image of any bulk operator. Furthermore, we provide an explicit methodology for calculating the correlation functions in an efficient manner. Our findings highlight the physical aspects of the relation between bulk and boundary within the tensor network models, contributing to the understanding and simulation of holographic principles in quantum information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02029 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bulk-boundary correspondence from hyper-invariant tensor networks Bistroń, Rafał Hontarenko, Mykhailo Życzkowski, Karol Quantum Physics High Energy Physics - Theory We introduce a tensor network designed to faithfully simulate the AdS/CFT correspondence, akin to the multi-scale entanglement renormalization ansatz (MERA), following hyper-invariant tensor network. The proposed construction integrates bulk indices within the network architecture to uphold the key features of the HaPPY code, including complementary recovery. This framework accurately reproduces the boundary conformal field theory's (CFT) two- and three-point correlation functions, while considering the image of any bulk operator. Furthermore, we provide an explicit methodology for calculating the correlation functions in an efficient manner. Our findings highlight the physical aspects of the relation between bulk and boundary within the tensor network models, contributing to the understanding and simulation of holographic principles in quantum information. |
| title | Bulk-boundary correspondence from hyper-invariant tensor networks |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.02029 |