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Journal Article

Ryu-Takayanagi Formula for Symmetric Random Tensor Networks

MPS-Authors

Chirco,  Goffredo
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Oriti,  Daniele
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Zhang mi,  Mingyi
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1711.09941.pdf
(Preprint), 468KB

PRD.97.126002.pdf
(Publisher version), 463KB

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Citation

Chirco, G., Oriti, D., & Zhang mi, M. (2018). Ryu-Takayanagi Formula for Symmetric Random Tensor Networks. Physical Review D, 97: 126002. doi:10.1103/PhysRevD.97.126002.


Cite as: https://hdl.handle.net/21.11116/0000-0000-3D42-2
Abstract
We consider the special case of Random Tensor Networks (RTN) endowed with gauge symmetry constraints on each tensor. We compute the R\`enyi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background independent quantum gravity, and for importing quantum gravity tools in tensor network research.