Negativity spectra in random tensor networks and holography
Abstract Negativity is a measure of entanglement that can be used both in pure and mixed states. The negativity spectrum is the spectrum of eigenvalues of the partially transposed density matrix, and characterizes the degree and “phase” of entanglement. For pure states, it is simply determined by th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2022)076 |
| _version_ | 1818331996549545984 |
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| author | Jonah Kudler-Flam Vladimir Narovlansky Shinsei Ryu |
| author_facet | Jonah Kudler-Flam Vladimir Narovlansky Shinsei Ryu |
| author_sort | Jonah Kudler-Flam |
| collection | DOAJ |
| description | Abstract Negativity is a measure of entanglement that can be used both in pure and mixed states. The negativity spectrum is the spectrum of eigenvalues of the partially transposed density matrix, and characterizes the degree and “phase” of entanglement. For pure states, it is simply determined by the entanglement spectrum. We use a diagrammatic method complemented by a modification of the Ford-Fulkerson algorithm to find the negativity spectrum in general random tensor networks with large bond dimensions. In holography, these describe the entanglement of fixed-area states. It was found that many fixed-area states have a negativity spectrum given by a semi-circle. More generally, we find new negativity spectra that appear in random tensor networks, as well as in phase transitions in holographic states, wormholes, and holographic states with bulk matter. The smallest random tensor network is the same as a micro-canonical version of Jackiw-Teitelboim (JT) gravity decorated with end-of-the-world branes. We consider the semi-classical negativity of Hawking radiation and find that contributions from islands should be included. We verify this in the JT gravity model, showing the Euclidean wormhole origin of these contributions. |
| first_indexed | 2024-12-13T13:28:43Z |
| format | Article |
| id | doaj.art-7a9b202313d74fcaaa29c86b47580b46 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T13:28:43Z |
| publishDate | 2022-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-7a9b202313d74fcaaa29c86b47580b462022-12-21T23:44:13ZengSpringerOpenJournal of High Energy Physics1029-84792022-02-012022217410.1007/JHEP02(2022)076Negativity spectra in random tensor networks and holographyJonah Kudler-Flam0Vladimir Narovlansky1Shinsei Ryu2Kadanoff Center for Theoretical Physics, University of ChicagoPrinceton Center for Theoretical Science, Princeton UniversityPrinceton Center for Theoretical Science, Princeton UniversityAbstract Negativity is a measure of entanglement that can be used both in pure and mixed states. The negativity spectrum is the spectrum of eigenvalues of the partially transposed density matrix, and characterizes the degree and “phase” of entanglement. For pure states, it is simply determined by the entanglement spectrum. We use a diagrammatic method complemented by a modification of the Ford-Fulkerson algorithm to find the negativity spectrum in general random tensor networks with large bond dimensions. In holography, these describe the entanglement of fixed-area states. It was found that many fixed-area states have a negativity spectrum given by a semi-circle. More generally, we find new negativity spectra that appear in random tensor networks, as well as in phase transitions in holographic states, wormholes, and holographic states with bulk matter. The smallest random tensor network is the same as a micro-canonical version of Jackiw-Teitelboim (JT) gravity decorated with end-of-the-world branes. We consider the semi-classical negativity of Hawking radiation and find that contributions from islands should be included. We verify this in the JT gravity model, showing the Euclidean wormhole origin of these contributions.https://doi.org/10.1007/JHEP02(2022)076AdS-CFT CorrespondenceGauge-Gravity CorrespondenceRandom Systems |
| spellingShingle | Jonah Kudler-Flam Vladimir Narovlansky Shinsei Ryu Negativity spectra in random tensor networks and holography Journal of High Energy Physics AdS-CFT Correspondence Gauge-Gravity Correspondence Random Systems |
| title | Negativity spectra in random tensor networks and holography |
| title_full | Negativity spectra in random tensor networks and holography |
| title_fullStr | Negativity spectra in random tensor networks and holography |
| title_full_unstemmed | Negativity spectra in random tensor networks and holography |
| title_short | Negativity spectra in random tensor networks and holography |
| title_sort | negativity spectra in random tensor networks and holography |
| topic | AdS-CFT Correspondence Gauge-Gravity Correspondence Random Systems |
| url | https://doi.org/10.1007/JHEP02(2022)076 |
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