Abstract
Recent work has shown how to understand the Page curve of an evaporating black hole from replica wormholes. However, more detailed information about the structure of its quantum state is needed to fully understand the dynamics of black hole evaporation. Here we study entanglement negativity, an important measure of quantum entanglement in mixed states, in a couple of toy models of evaporating black holes. We find four phases dominated by different types of geometries: the disconnected, cyclically connected, anti-cyclically connected, and pairwise connected geometries. The last of these geometries are new replica wormholes that break the replica symmetry spontaneously. We also analyze the transitions between these four phases by summing more generic replica geometries using a Schwinger-Dyson equation. In particular, we find enhanced corrections to various negativity measures near the transition between the cyclic and pairwise phase.
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G. Penington, S. H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, JHEP 03 (2022) 205 [arXiv:1911.11977] [INSPIRE].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05 (2020) 013 [arXiv:1911.12333] [INSPIRE].
N. Engelhardt and A. C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].
X. Dong and A. Lewkowycz, Entropy, Extremality, Euclidean Variations, and the Equations of Motion, JHEP 01 (2018) 081 [arXiv:1705.08453] [INSPIRE].
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09 (2020) 002 [arXiv:1905.08255] [INSPIRE].
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, JHEP 12 (2019) 063 [arXiv:1905.08762] [INSPIRE].
G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A 65 (2002) 032314 [quant-ph/0102117] [INSPIRE].
M. B. Plenio, Logarithmic Negativity: A Full Entanglement Monotone That is not Convex, Phys. Rev. Lett. 95 (2005) 090503 [quant-ph/0505071] [INSPIRE].
K. Audenaert, M. Plenio and J. Eisert, Entanglement cost under positive-partial-transpose-preserving operations, Phys. Rev. Lett. 90 (2003) 027901 [quant-ph/0207146].
P. Calabrese, J. Cardy and E. Tonni, Entanglement negativity in quantum field theory, Phys. Rev. Lett. 109 (2012) 130502 [arXiv:1206.3092] [INSPIRE].
P. Calabrese, J. Cardy and E. Tonni, Entanglement negativity in extended systems: A field theoretical approach, J. Stat. Mech. 1302 (2013) P02008 [arXiv:1210.5359] [INSPIRE].
M. Rangamani and M. Rota, Comments on Entanglement Negativity in Holographic Field Theories, JHEP 10 (2014) 060 [arXiv:1406.6989] [INSPIRE].
P. Calabrese, J. Cardy and E. Tonni, Finite temperature entanglement negativity in conformal field theory, J. Phys. A 48 (2015) 015006 [arXiv:1408.3043] [INSPIRE].
P. Chaturvedi, V. Malvimat and G. Sengupta, Entanglement negativity, Holography and Black holes, Eur. Phys. J. C 78 (2018) 499 [arXiv:1602.01147] [INSPIRE].
P. Chaturvedi, V. Malvimat and G. Sengupta, Holographic Quantum Entanglement Negativity, JHEP 05 (2018) 172 [arXiv:1609.06609] [INSPIRE].
P. Jain, V. Malvimat, S. Mondal and G. Sengupta, Holographic entanglement negativity conjecture for adjacent intervals in AdS3/CFT2, Phys. Lett. B 793 (2019) 104 [arXiv:1707.08293] [INSPIRE].
P. Jain, V. Malvimat, S. Mondal and G. Sengupta, Holographic entanglement negativity for adjacent subsystems in AdSd+1/CFTd, Eur. Phys. J. Plus 133 (2018) 300 [arXiv:1708.00612] [INSPIRE].
V. Malvimat and G. Sengupta, Entanglement negativity at large central charge, Phys. Rev. D 103 (2021) 106003 [arXiv:1712.02288] [INSPIRE].
J. Kudler-Flam and S. Ryu, Entanglement negativity and minimal entanglement wedge cross sections in holographic theories, Phys. Rev. D 99 (2019) 106014 [arXiv:1808.00446] [INSPIRE].
K. Tamaoka, Entanglement Wedge Cross Section from the Dual Density Matrix, Phys. Rev. Lett. 122 (2019) 141601 [arXiv:1809.09109] [INSPIRE].
V. Malvimat, S. Mondal, B. Paul and G. Sengupta, Holographic entanglement negativity for disjoint intervals in AdS3/CFT2, Eur. Phys. J. C 79 (2019) 191 [arXiv:1810.08015] [INSPIRE].
J. Kudler-Flam, M. Nozaki, S. Ryu and M. T. Tan, Quantum vs. classical information: operator negativity as a probe of scrambling, JHEP 01 (2020) 031 [arXiv:1906.07639] [INSPIRE].
Y. Kusuki, J. Kudler-Flam and S. Ryu, Derivation of holographic negativity in AdS3/CFT2, Phys. Rev. Lett. 123 (2019) 131603 [arXiv:1907.07824] [INSPIRE].
J. Kumar Basak, H. Parihar, B. Paul and G. Sengupta, Holographic entanglement negativity for disjoint subsystems in AdSd+1/CFTd, arXiv:2001.10534 [INSPIRE].
J. Kumar Basak, V. Malvimat, H. Parihar, B. Paul and G. Sengupta, On minimal entanglement wedge cross section for holographic entanglement negativity, arXiv:2002.10272 [INSPIRE].
J. Kudler-Flam, Y. Kusuki and S. Ryu, The quasi-particle picture and its breakdown after local quenches: mutual information, negativity, and reflected entropy, JHEP 03 (2021) 146 [arXiv:2008.11266] [INSPIRE].
T.-C. Lu and T. Grover, Entanglement transitions as a probe of quasiparticles and quantum thermalization, Phys. Rev. B 102 (2020) 235110 [arXiv:2008.11727] [INSPIRE].
J. Kumar Basak, D. Basu, V. Malvimat, H. Parihar and G. Sengupta, Islands for entanglement negativity, SciPost Phys. 12 (2022) 003 [arXiv:2012.03983] [INSPIRE].
H. Shapourian, S. Liu, J. Kudler-Flam and A. Vishwanath, Entanglement Negativity Spectrum of Random Mixed States: A Diagrammatic Approach, PRX Quantum 2 (2021) 030347 [arXiv:2011.01277] [INSPIRE].
X. Dong, X.-L. Qi and M. Walter, Holographic entanglement negativity and replica symmetry breaking, JHEP 06 (2021) 024 [arXiv:2101.11029] [INSPIRE].
J. Kumar Basak, D. Basu, V. Malvimat, H. Parihar and G. Sengupta, Page curve for entanglement negativity through geometric evaporation, SciPost Phys. 12 (2022) 004 [arXiv:2106.12593] [INSPIRE].
S. Vardhan, J. Kudler-Flam, H. Shapourian and H. Liu, Bound entanglement in thermalized states and black hole radiation, arXiv:2110.02959 [INSPIRE].
X. Dong and H. Wang, Enhanced corrections near holographic entanglement transitions: a chaotic case study, JHEP 11 (2020) 007 [arXiv:2006.10051] [INSPIRE].
D. Marolf, S. Wang and Z. Wang, Probing phase transitions of holographic entanglement entropy with fixed area states, JHEP 12 (2020) 084 [arXiv:2006.10089] [INSPIRE].
D. Marolf and H. Maxfield, Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information, JHEP 08 (2020) 044 [arXiv:2002.08950] [INSPIRE].
J. Kudler-Flam, V. Narovlansky and S. Ryu, Negativity spectra in random tensor networks and holography, JHEP 02 (2022) 076 [arXiv:2109.02649] [INSPIRE].
S. Vardhan, J. Kudler-Flam, H. Shapourian and H. Liu, Mixed-state entanglement and information recovery in thermalized states and evaporating black holes, arXiv:2112.00020 [INSPIRE].
A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77 (1996) 1413 [quant-ph/9604005] [INSPIRE].
M. Horodecki, P. Horodecki and R. Horodecki, On the necessary and sufficient conditions for separability of mixed quantum states, Phys. Lett. A 223 (1996) 1 [quant-ph/9605038] [INSPIRE].
X. Dong, The Gravity Dual of Renyi Entropy, Nature Commun. 7 (2016) 12472 [arXiv:1601.06788] [INSPIRE].
I. Kourkoulou and J. Maldacena, Pure states in the SYK model and nearly-AdS2 gravity, arXiv:1707.02325 [INSPIRE].
A. Almheiri, Holographic Quantum Error Correction and the Projected Black Hole Interior, arXiv:1810.02055 [INSPIRE].
T. Banica and I. Nechita, Asymptotic eigenvalue distributions of block-transposed wishart matrices, J. Theor. Probab. 26 (2013) 855 [arXiv:1105.2556].
C. Akers and P. Rath, Holographic Renyi Entropy from Quantum Error Correction, JHEP 05 (2019) 052 [arXiv:1811.05171] [INSPIRE].
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Dong, X., McBride, S. & Weng, W.W. Replica wormholes and holographic entanglement negativity. J. High Energ. Phys. 2022, 94 (2022). https://doi.org/10.1007/JHEP06(2022)094
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DOI: https://doi.org/10.1007/JHEP06(2022)094