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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Bibliographic Details
Main Authors: Alexey Milekhin, Pratik Rath, Wayne Weng
Format: Article
Language:English
Published: SpringerOpen 2025-02-01
Series:Journal of High Energy Physics
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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.
ISSN:1029-8479