On the computable cross norm in tensor networks and holography
Abstract The computable cross norm or realignment (CCNR) was recently discussed in ref. [1] as a measure of multipartite entanglement in a condensed matter context. In this short note, we point out that it is closely related to the (2, n)-Rényi reflected entropy, which has been studied in the contex...
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SpringerOpen
2025-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP02(2025)165 |
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| author | Alexey Milekhin Pratik Rath Wayne Weng |
| author_facet | Alexey Milekhin Pratik Rath Wayne Weng |
| author_sort | Alexey Milekhin |
| collection | DOAJ |
| description | Abstract The computable cross norm or realignment (CCNR) was recently discussed in ref. [1] as a measure of multipartite entanglement in a condensed matter context. In this short note, we point out that it is closely related to the (2, n)-Rényi reflected entropy, which has been studied in the context of AdS/CFT. We discuss the calculation of the CCNR in random tensor networks as well as holographic CFTs. The holographic dual involves a backreacted entanglement wedge cross section in a geometry sourced by Rényi-2 cosmic branes. We perform explicit calculations for two intervals in a hyperbolic random tensor network as well the vacuum state of a 2D holographic CFT, and analyze the occurence of a connected-to-disconnected phase transition. The example illustrates the validity of the proposal for analytic continuation in holography for arbitrary values of Rényi parameter n. We comment on a symmetry-resolved generalization of this quantity. |
| format | Article |
| id | doaj-art-a8ddad91fd9c4f4890c5a33fcb995cd3 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-a8ddad91fd9c4f4890c5a33fcb995cd32025-08-20T02:16:22ZengSpringerOpenJournal of High Energy Physics1029-84792025-02-012025211710.1007/JHEP02(2025)165On the computable cross norm in tensor networks and holographyAlexey Milekhin0Pratik Rath1Wayne Weng2Department of Physics, University of CaliforniaDepartment of Physics, University of CaliforniaDepartment of Physics, University of CaliforniaAbstract The computable cross norm or realignment (CCNR) was recently discussed in ref. [1] as a measure of multipartite entanglement in a condensed matter context. In this short note, we point out that it is closely related to the (2, n)-Rényi reflected entropy, which has been studied in the context of AdS/CFT. We discuss the calculation of the CCNR in random tensor networks as well as holographic CFTs. The holographic dual involves a backreacted entanglement wedge cross section in a geometry sourced by Rényi-2 cosmic branes. We perform explicit calculations for two intervals in a hyperbolic random tensor network as well the vacuum state of a 2D holographic CFT, and analyze the occurence of a connected-to-disconnected phase transition. The example illustrates the validity of the proposal for analytic continuation in holography for arbitrary values of Rényi parameter n. We comment on a symmetry-resolved generalization of this quantity.https://doi.org/10.1007/JHEP02(2025)165AdS-CFT CorrespondenceGauge-Gravity Correspondence |
| spellingShingle | Alexey Milekhin Pratik Rath Wayne Weng On the computable cross norm in tensor networks and holography Journal of High Energy Physics AdS-CFT Correspondence Gauge-Gravity Correspondence |
| title | On the computable cross norm in tensor networks and holography |
| title_full | On the computable cross norm in tensor networks and holography |
| title_fullStr | On the computable cross norm in tensor networks and holography |
| title_full_unstemmed | On the computable cross norm in tensor networks and holography |
| title_short | On the computable cross norm in tensor networks and holography |
| title_sort | on the computable cross norm in tensor networks and holography |
| topic | AdS-CFT Correspondence Gauge-Gravity Correspondence |
| url | https://doi.org/10.1007/JHEP02(2025)165 |
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