Islands for Entanglement Negativity

Abstract

We advance two alternative proposals for the island contributions to the entanglement negativity of various pure and mixed state configurations in quantum field theories coupled to semiclassical gravity. The first construction involves the extremization of an algebraic sum of the generalized Renyi entropies of order half. The second proposal involves the extremization of the sum of the effective entanglement negativity of quantum matter fields and the backreacted area of a cosmic brane spanning the entanglement wedge cross section which also extremizes the generalized Renyi reflected entropy of order half. These proposals are utilized to obtain the island contributions to the entanglement negativity of various pure and mixed state configurations involving the bath systems coupled to extremal and non-extremal black holes in JT gravity demonstrating an exact match with each other. Furthermore, the results from both the proposals match precisely with the island contribution to half the Renyi reflected entropy of order half providing a strong consistency check. We then allude to a possible doubly holographic picture of our island proposals and provide a derivation of the first proposal by determining the corresponding replica wormhole contributions.

81 pages, 29 figures, 1 appendix, major modifications, section and references added

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Cited by in corpus (22)

• Inconsistency of Islands in Theories with Long-Range Gravity
• Dirichlet Baths and the Not-so-Fine-Grained Page Curve
• Islands in charged linear dilaton black holes
• The universality of islands outside the horizon
• Defect Extremal Surface for Reflected Entropy
• Holographic spacetime, black holes and quantum error correcting codes: A review
• Entanglement Wedge in Flat Holography and Entanglement Negativity
• Partial islands and subregion complexity in geometric secret-sharing model
• Replica Wormholes and Holographic Entanglement Negativity
• Page Curve for Entanglement Negativity through Geometric Evaporation
• Page Curve of Effective Hawking Radiation
• Negativity Spectra in Random Tensor Networks and Holography
• Ephemeral Islands, Plunging Quantum Extremal Surfaces and BCFT channels
• Hints of Gravitational Ergodicity: Berry's Ensemble and the Universality of the Semi-Classical Page Curve
• Islands in the Stream of Hawking Radiation
• Grey-body Factors, Irreversibility and Multiple Island Saddles
• Entanglement between two evaporating black holes
• A comment on a fine-grained description of evaporating black holes with baby universes
• Covariant holographic negativity from the entanglement wedge in AdS${}_3/$CFT${}_2$
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• Entanglement Negativity in Flat Holography
• Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge