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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2022
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| Accès en ligne: | https://arxiv.org/abs/2212.11978 |
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| _version_ | 1866916526324449280 |
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| author | Milekhin, Alexey Rath, Pratik Weng, Wayne |
| author_facet | Milekhin, Alexey Rath, Pratik Weng, Wayne |
| contents | The Computable Cross Norm (CCNR) was recently discussed in Ref.~\cite{Yin:2022toc} 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11978 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Computable Cross Norm in Tensor Networks and Holography Milekhin, Alexey Rath, Pratik Weng, Wayne High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons General Relativity and Quantum Cosmology Quantum Physics The Computable Cross Norm (CCNR) was recently discussed in Ref.~\cite{Yin:2022toc} 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. |
| title | Computable Cross Norm in Tensor Networks and Holography |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2212.11978 |