Abstract
This paper is an attempt to extend the recent understanding of the Page curve for evaporating black holes to more general systems coupled to a heat bath. Although calculating the von Neumann entropy by the replica trick is usually a challenge, we have identified two solvable cases. For the initial section of the Page curve, we sum up the perturbation series in the system-bath coupling κ; the most interesting contribution is of order 2s, where s is the number of replicas. For the saturated regime, we consider the effect of an external impulse on the entropy at a later time and relate it to OTOCs. A significant simplification occurs in the maximal chaos case such that the effect may be interpreted in terms of an intermediate object, analogous to the branching surface of a replica wormhole.
Change history
17 August 2022
An Erratum to this paper has been published: https://doi.org/10.1007/JHEP08(2022)154
References
D. N. Page, Information in black hole radiation, Phys. Rev. Lett. 71 (1993) 3743 [hep-th/9306083] [INSPIRE].
T. Dray and G. ’t Hooft, The gravitational shock wave of a massless particle, Nucl. Phys. B 253 (1985) 173 [INSPIRE].
G. ’t Hooft, The black hole interpretation of string theory, Nucl. Phys. B 335 (1990) 138 [INSPIRE].
S. H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [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].
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].
Y. Chen, X.-L. Qi and P. Zhang, Replica wormhole and information retrieval in the SYK model coupled to Majorana chains, JHEP 06 (2020) 121 [arXiv:2003.13147] [INSPIRE].
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev, Hidden correlations in the Hawking radiation and thermal noise, talk at KITP, http://online.kitp.ucsb.edu/online/joint98/kitaev/, University of California, Santa Barbara, CA, U.S.A., 12 February 2015.
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [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].
J. Maldacena, S. H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [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].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2011.09622
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Dadras, P., Kitaev, A. Perturbative calculations of entanglement entropy. J. High Energ. Phys. 2021, 198 (2021). https://doi.org/10.1007/JHEP03(2021)198
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2021)198
Keywords
- AdS-CFT Correspondence
- Black Holes
- 2D Gravity