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: Alexey Milekhin, Pratik Rath, Wayne Weng
Format: Article
Language:English
Published: SpringerOpen 2025-02-01
Series:Journal of High Energy Physics
Subjects:
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.
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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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