Reflected entropy in random tensor networks

Abstract

In holographic theories, the reflected entropy has been shown to be dual to the area of the entanglement wedge cross section. We study the same problem in random tensor networks demonstrating an equivalent duality. For a single random tensor we analyze the important non-perturbative effects that smooth out the discontinuity in the reflected entropy across the Page phase transition. By summing over all such effects, we obtain the reflected entanglement spectrum analytically, which agrees well with numerical studies. This motivates a prescription for the analytic continuation required in computing the reflected entropy and its Rényi generalization which resolves an order of limits issue previously identified in the literature. We apply this prescription to hyperbolic tensor networks and find answers consistent with holographic expectations. In particular, the random tensor network has the same non-trivial tripartite entanglement structure expected from holographic states. We furthermore show that the reflected Rényi spectrum is not flat, in sharp contrast to the usual Rényi spectrum of these networks. We argue that the various distinct contributions to the reflected entanglement spectrum can be organized into approximate superselection sectors. We interpret this as resulting from an effective description of the canonically purified state as a superposition of distinct tensor network states. Each network is constructed by doubling and gluing various candidate entanglement wedges of the original network. The superselection sectors are labelled by the different cross-sectional areas of these candidate entanglement wedges.

58 pages + appendices, 24 figures, v2: fixed typos and added 1 figure, v3: typo fixed

References in corpus (8)

• Leading order corrections to the quantum extremal surface prescription
• Some general properties of unified entropies
• Entanglement negativity spectrum of random mixed states: A diagrammatic approach
• Probing phase transitions of holographic entanglement entropy with fixed area states
• Enhanced corrections near holographic entanglement transitions: a chaotic case study
• Negativity Spectra in Random Tensor Networks and Holography
• Complex Entangling Surfaces for AdS and Lifshitz Black Holes?
• The Markov gap for geometric reflected entropy

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• Typical Correlation Length of Sequentially Generated Tensor Network States
• Reflected Entropy for Communicating Black Holes I: Karch-Randall Braneworlds
• Universal entanglement and correlation measure in two-dimensional conformal field theories
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• Bounding entanglement wedge cross sections
• Reflected entropy in Galilean conformal field theories and flat holography
• The Reflected Entanglement Spectrum for Free Fermions
• Large and Small Corrections to the JLMS Formula from Replica Wormholes
• Encoded information of mixed correlations: the views from one dimension higher
• The Holographic Map of an Evaporating Black Hole