Toy models of holographic duality between local Hamiltonians
Abstract Holographic quantum error correcting codes (HQECC) have been proposed as toy models for the AdS/CFT correspondence, and exhibit many of the features of the duality. HQECC give a mapping of states and observables. However, they do not map local bulk Hamiltonians to local Hamiltonians on the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP08(2019)017 |
| _version_ | 1819174931890438144 |
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| author | Tamara Kohler Toby Cubitt |
| author_facet | Tamara Kohler Toby Cubitt |
| author_sort | Tamara Kohler |
| collection | DOAJ |
| description | Abstract Holographic quantum error correcting codes (HQECC) have been proposed as toy models for the AdS/CFT correspondence, and exhibit many of the features of the duality. HQECC give a mapping of states and observables. However, they do not map local bulk Hamiltonians to local Hamiltonians on the boundary. In this work, we combine HQECC with Hamiltonian simulation theory to construct a bulk-boundary mapping between local Hamiltonians, whilst retaining all the features of the HQECC duality. This allows us to construct a duality between models, encompassing the relationship between bulk and boundary energy scales and time dynamics. It also allows us to construct a map in the reverse direction: from local boundary Hamiltonians to the corresponding local Hamiltonian in the bulk. Under this boundary-to-bulk mapping, the bulk geometry emerges as an approximate, low-energy, effective theory living in the code-space of an (approximate) HQECC on the boundary. At higher energy scales, this emergent bulk geometry is modified in a way that matches the toy models of black holes proposed previously for HQECC. Moreover, the duality on the level of dynamics shows how these toy-model black holes can form dynamically. |
| first_indexed | 2024-12-22T20:46:49Z |
| format | Article |
| id | doaj.art-fc8d96dc570f4c8c85b6913033c3b358 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T20:46:49Z |
| publishDate | 2019-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-fc8d96dc570f4c8c85b6913033c3b3582022-12-21T18:13:12ZengSpringerOpenJournal of High Energy Physics1029-84792019-08-012019816410.1007/JHEP08(2019)017Toy models of holographic duality between local HamiltoniansTamara Kohler0Toby Cubitt1Department of Computer Science, University College LondonDepartment of Computer Science, University College LondonAbstract Holographic quantum error correcting codes (HQECC) have been proposed as toy models for the AdS/CFT correspondence, and exhibit many of the features of the duality. HQECC give a mapping of states and observables. However, they do not map local bulk Hamiltonians to local Hamiltonians on the boundary. In this work, we combine HQECC with Hamiltonian simulation theory to construct a bulk-boundary mapping between local Hamiltonians, whilst retaining all the features of the HQECC duality. This allows us to construct a duality between models, encompassing the relationship between bulk and boundary energy scales and time dynamics. It also allows us to construct a map in the reverse direction: from local boundary Hamiltonians to the corresponding local Hamiltonian in the bulk. Under this boundary-to-bulk mapping, the bulk geometry emerges as an approximate, low-energy, effective theory living in the code-space of an (approximate) HQECC on the boundary. At higher energy scales, this emergent bulk geometry is modified in a way that matches the toy models of black holes proposed previously for HQECC. Moreover, the duality on the level of dynamics shows how these toy-model black holes can form dynamically.http://link.springer.com/article/10.1007/JHEP08(2019)017AdS-CFT CorrespondenceBlack Holes |
| spellingShingle | Tamara Kohler Toby Cubitt Toy models of holographic duality between local Hamiltonians Journal of High Energy Physics AdS-CFT Correspondence Black Holes |
| title | Toy models of holographic duality between local Hamiltonians |
| title_full | Toy models of holographic duality between local Hamiltonians |
| title_fullStr | Toy models of holographic duality between local Hamiltonians |
| title_full_unstemmed | Toy models of holographic duality between local Hamiltonians |
| title_short | Toy models of holographic duality between local Hamiltonians |
| title_sort | toy models of holographic duality between local hamiltonians |
| topic | AdS-CFT Correspondence Black Holes |
| url | http://link.springer.com/article/10.1007/JHEP08(2019)017 |
| work_keys_str_mv | AT tamarakohler toymodelsofholographicdualitybetweenlocalhamiltonians AT tobycubitt toymodelsofholographicdualitybetweenlocalhamiltonians |