On the computable cross norm in tensor networks and holography
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1.
University of California, Santa Barbara
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2.
California Institute of Technology
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3.
University of California, Berkeley
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4.
Cornell University
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.
Copyright and License (English)
© 2025, The Author(s). Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Acknowledgement
We would like to thank Eugenia Colafranceschi, Xi Dong, Sean McBride and Amir Tajdini for comments. PR is supported in part by a grant from the Simons Foundation, by funds from UCSB, the Berkeley Center for Theoretical Physics; by the Department of Energy, Office of Science, Office of High Energy Physics under QuantISED Award DE-SC0019380, under contract DE-AC02-05CH11231 and by the National Science Foundation under Award Number 2112880. This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-19-1-0360.
Additional Information
ArXiv ePrint: 2212.11978
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JHEP02(2025)165.pdf
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- Discussion Paper: arXiv:2212.11978 (arXiv)
Funding
- United States Air Force Office of Scientific Research
- FA9550-19-1-0360
- National Science Foundation
- 2112880
- Office of High Energy Physics
- QuantISED Award DE-SC0019380