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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-02-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2025)165 |
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| Summary: | 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. |
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| ISSN: | 1029-8479 |