We investigate multipartite entanglement in quantum geometry states described by loop quantum gravity spin networks. We focus on states corresponding to bounded regions of 3D spacelike slices of spacetime with nonvanishing intrinsic curvature, realized via spin networks defined on a graph with nontrivial $SU(2)$ holonomies. The presence of intrinsic curvature in the region is encoded—via coarse graining—into tag spins attached to the vertices of the graph. The resulting states are generalized bulk-to-boundary maps defined in an extended boundary Hilbert space comprised by the spin representations carried by the tags and by the uncontracted edges at the boundary. We consider a tripartition of a random quantum geometry state in the extended-boundary space consisting of a bipartite boundary subsystem and a bulk-tags complement, and we propose a measure of logarithmic negativity to study the change in the entanglement phases of the boundary marginal mixed state, while varying the dimension of the bulk curvature environment. In the large spin regime, we find that the typical entanglement negativity is well described by the generalized Page curve of a tripartite random state. In particular, we find area scaling behavior of negativity for small curvature, while for large curvature the negativity vanishes, suggesting an effective thermalization of the boundary. Remarkably, the positive partial transpose character of the mixed boundary state corresponds to a change in the effective topology of the network, with the two boundary subregions becoming disconnected.

• Received 8 May 2023
• Accepted 26 July 2023

DOI:https://doi.org/10.1103/PhysRevD.108.046010

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Published by the American Physical Society