Abstract
Motivated by recent studies of the information paradox in (1+1)-D anti-de Sitter spacetime with a bath described by a (1+1)-D conformal field theory, we study the dynamics of second Ŕenyi entropy of the Sachdev-Ye-Kitaev (SYK) model (χ) coupled to a Majorana chain bath (ψ). The system is prepared in the thermofield double (TFD) state and then evolved by HL + HR. For small system-bath coupling, we find that the second Rényi entropy \( {S}_{\upchi L,\upchi R}^{(2)} \) of the SYK model undergoes a first order transition during the evolution. In the sense of holographic duality, the long-time solution corresponds to a “replica wormhole”. The transition time corresponds to the Page time of a black hole coupled to a thermal bath. We further study the information scrambling and retrieval by introducing a classical control bit, which controls whether or not we add a perturbation in the SYK system. The mutual information between the bath and the control bit shows a positive jump at the Page time, indicating that the entanglement wedge of the bath includes an island in the holographic bulk.
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References
S.W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199.
D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [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].
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, 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].
A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, JHEP 03 (2020) 149 [arXiv:1908.10996] [INSPIRE].
A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon, arXiv:1910.11077 [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].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, arXiv:1911.11977 [INSPIRE].
C. Akers, S. Leichenauer and A. Levine, Large Breakdowns of Entanglement Wedge Reconstruction, Phys. Rev. D 100 (2019) 126006 [arXiv:1908.03975] [INSPIRE].
Z. Fu and D. Marolf, Bag-of-gold spacetimes, Euclidean wormholes and inflation from domain walls in AdS/CFT, JHEP 11 (2019) 040 [arXiv:1909.02505] [INSPIRE].
C. Akers, N. Engelhardt and D. Harlow, Simple holographic models of black hole evaporation, arXiv:1910.00972 [INSPIRE].
M. Rozali, J. Sully, M. Van Raamsdonk, C. Waddell and D. Wakeham, Information radiation in BCFT models of black holes, JHEP 05 (2020) 004 [arXiv:1910.12836] [INSPIRE].
H.Z. Chen, Z. Fisher, J. Hernandez, R.C. Myers and S.-M. Ruan, Information Flow in Black Hole Evaporation, JHEP 03 (2020) 152 [arXiv:1911.03402] [INSPIRE].
R. Bousso and M. Tomašević, Unitarity From a Smooth Horizon?, arXiv:1911.06305 [INSPIRE].
A. Almheiri, R. Mahajan and J.E. Santos, Entanglement islands in higher dimensions, arXiv:1911.09666 [INSPIRE].
Y. Chen, Pulling Out the Island with Modular Flow, JHEP 03 (2020) 033 [arXiv:1912.02210] [INSPIRE].
D. Marolf and H. Maxfield, Transcending the ensemble: baby universes, spacetime wormholes and the order and disorder of black hole information, arXiv:2002.08950 [INSPIRE].
X. Dong, D. Harlow and A.C. Wall, Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality, Phys. Rev. Lett. 117 (2016) 021601 [arXiv:1601.05416] [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
Y. Chen, H. Zhai and P. Zhang, Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath, JHEP 07 (2017) 150 [arXiv:1705.09818] [INSPIRE].
P. Zhang, Evaporation dynamics of the Sachdev-Ye-Kitaev model, Phys. Rev. B 100 (2019) 245104 [arXiv:1909.10637] [INSPIRE].
A. Almheiri, A. Milekhin and B. Swingle, Universal Constraints on Energy Flow and SYK Thermalization, arXiv:1912.04912 [INSPIRE].
Y. Gu, A. Lucas and X.-L. Qi, Spread of entanglement in a Sachdev-Ye-Kitaev chain, JHEP 09 (2017) 120 [arXiv:1708.00871] [INSPIRE].
A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, May 27, 2015, University of California, Santa Barbara, U.S.A. (2015) [http://online.kitp.ucsb.edu/online/entangled15/kitaev2/].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE].
J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
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Chen, Y., Qi, XL. & Zhang, P. Replica wormhole and information retrieval in the SYK model coupled to Majorana chains. J. High Energ. Phys. 2020, 121 (2020). https://doi.org/10.1007/JHEP06(2020)121
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DOI: https://doi.org/10.1007/JHEP06(2020)121