Linear growth of entanglement entropy in holographic thermalization captured by horizon interiors and mutual information

Journal of High Energy Physics

Volumn 2013, Issue 9, 2013, Pages

  Li, Yong Zhuang ^a   Wu, Shao Feng ^a,b   Wang, Yong Qiang ^c   Yang, Guo Hong ^a,b  

^a SHANGHAI UNIVERSITY   (China)

^b Shanghai Key Lab for Astrophysics   (China)

^c LANZHOU UNIVERSITY   (China)

Author keywords

Black Holes; Classical Theories of Gravity; Gauge gravity correspondence; Holography and condensed matter physics (AdS CMT)

Indexed keywords

EID: 84884569145     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP09(2013)057     Document Type: Article

References (100)

1. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [ hep-th/9711200 ] [ INSPIRE ].
2. S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [ hep-th/9802109 ] [ INSPIRE ].
3. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [ hep-th/9802150 ] [ INSPIRE ].
4. F. Gelis, The early stages of a high energy heavy ion collision, J. Phys. Conf. Ser. 381 (2012) 012021 [ arXiv:1110.1544 ] [ INSPIRE ].
5. B. Müller and A. Schafer, Entropy creation in relativistic heavy ion collisions, Int. J. Mod. Phys. E 20 (2011) 2235 [ arXiv:1110.2378 ] [ INSPIRE ].
6. E. Iancu, QCD in heavy ion collisions, arXiv:1205.0579 [ INSPIRE ].
7. R. Baier, A.H. Mueller, D. Schiff and D. Son, 'Bottom up' thermalization in heavy ion collisions, Phys. Lett. B 502 (2001) 51 [ hep-ph/0009237 ] [ INSPIRE ].
8. A. Mueller, A. Shoshi and S. Wong, A possible modified 'bottom-up' thermalization in heavy ion collisions, Phys. Lett. B 632 (2006) 257 [ hep-ph/0505164 ] [ INSPIRE ].
9. S. Mondal, D. Sen and K. Sengupta, Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer, arXiv:0908.2922.
10. J. Dziarmaga, Dynamics of a quantum phase transition and relaxation to a steady state, Adv. Phys. 59 (2010) 1063 [ arXiv:0912.4034 ].
11. A. Polkovnikov, K. Sengupta, A. Silva and M. Vengalattore, Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83 (2011) 863 [ arXiv:1007.5331 ] [ INSPIRE ].
12. M.A. Nielsen and I.L. Chuang, Quantum computation and quantum information, Cambridge University Press, Cambridge U.K. (2000).
13. P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 06 (2004) P06002 [ hep-th/0405152 ] [ INSPIRE ].
14. A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96 (2006) 110404 [ hep-th/0510092 ] [ INSPIRE ].
15. M. Levin and X.-G. Wen, Detecting topological order in a ground state wave function, Phys. Rev. Lett. 96 (2006) 110405 [ cond-mat/0510613 ].
16. B. Hsu, M. Mulligan, E. Fradkin and E.-A. Kim, Universal entanglement entropy in 2D conformal quantum critical points, Phys. Rev. B 79 (2009) 115421 [ arXiv:0812.0203 ] [ INSPIRE ].
17. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [ hep-th/0603001 ] [ INSPIRE ].
18. S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [ hep-th/0605073 ] [ INSPIRE ].
19. T. Takayanagi, Entanglement entropy from a holographic viewpoint, Class. Quant. Grav. 29 (2012) 153001 [ arXiv:1204.2450 ] [ INSPIRE ].
20. A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [ arXiv:1304.4926 ] [ INSPIRE ].
21. M. Van Raamsdonk, Comments on quantum gravity and entanglement, arXiv:0907.2939 [ INSPIRE ].
22. M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav. 42 (2010) 2323 [Int. J. Mod. Phys. D 19 (2010) 2429] [arXiv:1005.3035] [ INSPIRE ].
23. H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [ arXiv:1102.0440 ] [ INSPIRE ].
24. E. Bianchi and R.C. Myers, On the architecture of spacetime geometry, arXiv:1212.5183 [ INSPIRE ].
25. V.E. Hubeny and M. Rangamani, Causal holographic information, JHEP 06 (2012) 114 [ arXiv:1204.1698 ] [ INSPIRE ].
26. V.E. Hubeny, M. Rangamani and E. Tonni, Thermalization of causal holographic information, JHEP 05 (2013) 136 [ arXiv:1302.0853 ] [ INSPIRE ].
27. B. Swingle, Entanglement renormalization and holography, Phys. Rev. D 86 (2012) 065007 [ arXiv:0905.1317 ] [ INSPIRE ].
28. B. Swingle, Constructing holographic spacetimes using entanglement renormalization, arXiv:1209.3304 [ INSPIRE ].
29. J. Molina-Vilaplana and P. Sodano, Holographic view on quantum correlations and mutual information between disjoint blocks of a quantum critical system, JHEP 10 (2011) 011 [ arXiv:1108.1277 ] [ INSPIRE ].
30. V. Balasubramanian, M.B. McDermott and M. Van Raamsdonk, Momentum-space entanglement and renormalization in quantum field theory, Phys. Rev. D 86 (2012) 045014 [ arXiv:1108.3568 ] [ INSPIRE ].
31. H. Matsueda, Scaling of entanglement entropy and hyperbolic geometry, arXiv:1112.5566 [ INSPIRE ].
32. M. Ishihara, F.-L. Lin and B. Ning, Refined holographic entanglement entropy for the AdS solitons and AdS black holes, Nucl. Phys. B 872 (2013) 392 [ arXiv:1203.6153 ] [ INSPIRE ].
33. H. Matsueda, M. Ishihara and Y. Hashizume, Tensor network and black hole, arXiv:1208.0206 [ INSPIRE ].
34. M. Nozaki, S. Ryu and T. Takayanagi, Holographic geometry of entanglement renormalization in quantum field theories, JHEP 10 (2012) 193 [ arXiv:1208.3469 ] [ INSPIRE ].
35. M. Nozaki, T. Numasawa and T. Takayanagi, Holographic local quenches and entanglement density, JHEP 05 (2013) 080 [ arXiv:1302.5703 ] [ INSPIRE ].
36. T. Hartman and J. Maldacena, Time evolution of entanglement entropy from black hole interiors, JHEP 05 (2013) 014 [ arXiv:1303.1080 ] [ INSPIRE ].
37. G. Vidal, Entanglement renormalization, Phys. Rev. Lett. 99 (2007) 220405 [ cond-mat/0512165 ] [ INSPIRE ].
38. G. Vidal, Entanglement renormalization: an introduction, arXiv:0912.1651.
39. J. Haegeman, T.J. Osborne, H. Verschelde and F. Verstraete, Entanglement renormalization for quantum fields, Phys. Rev. Lett. 110 (2013) 100402 [ arXiv:1102.5524 ] [ INSPIRE ].
40. G. Evenbly and G. Vidal, Quantum criticality with the multi-scale entanglement renormalization ansatz, arXiv:1109.5334.
41. V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [ arXiv:0705.0016 ] [ INSPIRE ].
42. M.M. Wolf, F. Verstraete, M.B. Hastings and J.I. Cirac, Area laws in quantum systems: mutual information and correlations, Phys. Rev. Lett. 100 (2008) 070502 [ arXiv:0704.3906 ].
43. B. Swingle, Mutual information and the structure of entanglement in quantum field theory, arXiv:1010.4038 [ INSPIRE ].
44. S. Furukawa, V. Pasquier and J. Shiraishi, Mutual information and compactification radius in a c = 1 critical phase in one dimension, Phys. Rev. Lett. 102 (2009) 170602 [ arXiv:0809.5113 ] [ INSPIRE ].
45. P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory, J. Stat. Mech. 11 (2009) P11001 [ arXiv:0905.2069 ] [ INSPIRE ].
46. P. Calabrese, J. Cardy and E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory II, J. Stat. Mech. 01 (2011) P01021 [ arXiv:1011.5482 ] [ INSPIRE ].
47. M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [ arXiv:1006.0047 ] [ INSPIRE ].
48. V.E. Hubeny and M. Rangamani, Holographic entanglement entropy for disconnected regions, JHEP 03 (2008) 006 [ arXiv:0711.4118 ] [ INSPIRE ].
49. E. Tonni, Holographic entanglement entropy: near horizon geometry and disconnected regions, JHEP 05 (2011) 004 [ arXiv:1011.0166 ] [ INSPIRE ].
50. V. Balasubramanian, A. Bernamonti, N. Copland, B. Craps and F. Galli, Thermalization of mutual and tripartite information in strongly coupled two dimensional conformal field theories, Phys. Rev. D 84 (2011) 105017 [ arXiv:1110.0488 ] [ INSPIRE ].
51. A. Allais and E. Tonni, Holographic evolution of the mutual information, JHEP 01 (2012) 102 [ arXiv:1110.1607 ] [ INSPIRE ].
52. R. Callan, J.-Y. He and M. Headrick, Strong subadditivity and the covariant holographic entanglement entropy formula, JHEP 06 (2012) 081 [ arXiv:1204.2309 ] [ INSPIRE ].
53. W. Fischler and S. Kundu, Strongly coupled gauge theories: high and low temperature behavior of non-local observables, JHEP 05 (2013) 098 [ arXiv:1212.2643 ] [ INSPIRE ].
54. W. Fischler, A. Kundu and S. Kundu, Holographic mutual information at finite temperature, Phys. Rev. D 87 (2013) 126012 [ arXiv:1212.4764 ] [ INSPIRE ].
55. S. Bhattacharyya and S. Minwalla, Weak field black hole formation in asymptotically AdS spacetimes, JHEP 09 (2009) 034 [ arXiv:0904.0464 ] [ INSPIRE ].
56. S.R. Das, T. Nishioka and T. Takayanagi, Probe branes, time-dependent couplings and thermalization in AdS/CFT, JHEP 07 (2010) 071 [ arXiv:1005.3348 ] [ INSPIRE ].
57. H. Ebrahim and M. Headrick, Instantaneous thermalization in holographic plasmas, arXiv:1010.5443 [ INSPIRE ].
58. D. Garfinkle and L.A. Pando Zayas, Rapid thermalization in field theory from gravitational collapse, Phys. Rev. D 84 (2011) 066006 [ arXiv:1106.2339 ] [ INSPIRE ].
59. S.R. Das, Holographic quantum quench, J. Phys. Conf. Ser. 343 (2012) 012027 [ arXiv:1111.7275 ] [ INSPIRE ].
60. A. Buchel, L. Lehner and R.C. Myers, Thermal quenches in N = 2plasmas, JHEP 08 (2012) 049 [ arXiv:1206.6785 ] [ INSPIRE ].
61. X. Gao, A.M. Garcia-Garcia, H.B. Zeng and H.-Q. Zhang, Lack of thermalization in holographic superconductivity, arXiv:1212.1049 [ INSPIRE ].
62. W. Baron, D. Galante and M. Schvellinger, Dynamics of holographic thermalization, JHEP 03 (2013) 070 [ arXiv:1212.5234 ] [ INSPIRE ].
63. J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic evolution of entanglement entropy, JHEP 11 (2010) 149 [ arXiv:1006.4090 ] [ INSPIRE ].
64. J. Aparicio and E. Lopez, Evolution of two-point functions from holography, JHEP 12 (2011) 082 [ arXiv:1109.3571 ] [ INSPIRE ].
65. T. Albash and C.V. Johnson, evolution of holographic entanglement entropy after thermal and electromagnetic quenches, New J. Phys. 13 (2011) 045017 [ arXiv:1008.3027 ] [ INSPIRE ].
66. V. Balasubramanian et al., Thermalization of strongly coupled field theories, Phys. Rev. Lett. 106 (2011) 191601 [ arXiv:1012.4753 ] [ INSPIRE ].
67. V. Balasubramanian et al., Holographic thermalization, Phys. Rev. D 84 (2011) 026010 [ arXiv:1103.2683 ] [ INSPIRE ].
68. V. Keranen, E. Keski-Vakkuri and L. Thorlacius, Thermalization and entanglement following a non-relativistic holographic quench, Phys. Rev. D 85 (2012) 026005 [ arXiv:1110.5035 ] [ INSPIRE ].
69. D. Galante and M. Schvellinger, Thermalization with a chemical potential from AdS spaces, JHEP 07 (2012) 096 [ arXiv:1205.1548 ] [ INSPIRE ].
70. E. Caceres and A. Kundu, Holographic thermalization with chemical potential, JHEP 09 (2012) 055 [ arXiv:1205.2354 ] [ INSPIRE ].
71. E. Caceres, A. Kundu, J.F. Pedraza and W. Tangarife, Strong subadditivity, null energy condition and charged black holes, arXiv:1304.3398 [ INSPIRE ].
72. X. Zeng and W. Liu, Holographic thermalization in Gauss-Bonnet gravity, arXiv:1305.4841 [ INSPIRE ].
73. S. Lin and E. Shuryak, Toward the AdS/CFT gravity dual for high energy collisions. 3. Gravitationally collapsing shell and quasiequilibrium, Phys. Rev. D 78 (2008) 125018 [ arXiv:0808.0910 ] [ INSPIRE ].
74. P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 04 (2005) P04010 [ cond-mat/0503393 ] [ INSPIRE ].
75. P. Calabrese and J. Cardy, Quantum quenches in extended systems, J. Stat. Mech. 06 (2007) P06008 [ arXiv:0704.1880 ] [ INSPIRE ].
76. P. Billingsley, Ergodic theory and information, Wiley, New York U.S.A. (1965).
77. V. Latora and M. Baranger, Kolmogorov-Sinai entropy rate versus physical entropy, Phys. Rev. Lett. 82 (1999) 520 [ chao-dyn/9806006 ].
78. J. Bolte, B. Müller and A. Schafer, Ergodic properties of classical SU(2) lattice gauge theory, Phys. Rev. D 61 (2000) 054506 [ hep-lat/9906037 ] [ INSPIRE ].
79. T. Kunihiro et al., Chaotic behavior in classical Yang-Mills dynamics, Phys. Rev. D 82 (2010) 114015 [ arXiv:1008.1156 ] [ INSPIRE ].
80. D.V. Fursaev, Proof of the holographic formula for entanglement entropy, JHEP 09 (2006) 018 [ hep-th/0606184 ] [ INSPIRE ].
81. J. de Boer, M. Kulaxizi and A. Parnachev, Holographic entanglement entropy in Lovelock gravities, JHEP 07 (2011) 109 [ arXiv:1101.5781 ] [ INSPIRE ].
82. L.-Y. Hung, R.C. Myers and M. Smolkin, On holographic entanglement entropy and higher curvature gravity, JHEP 04 (2011) 025 [ arXiv:1101.5813 ] [ INSPIRE ].
83. A. Bhattacharyya, A. Kaviraj and A. Sinha, Entanglement entropy in higher derivative holography, JHEP 08 (2013) 012 [ arXiv:1305.6694 ] [ INSPIRE ].
84. C.T. Asplund and S.G. Avery, Evolution of entanglement entropy in the D1-D5 brane system, Phys. Rev. D 84 (2011) 124053 [ arXiv:1108.2510 ] [ INSPIRE ].
85. P. Basu and S.R. Das, Quantum quench across a holographic critical point, JHEP 01 (2012) 103 [ arXiv:1109.3909 ] [ INSPIRE ].
86. A. Buchel, L. Lehner, R.C. Myers and A. van Niekerk, Quantum quenches of holographic plasmas, JHEP 05 (2013) 067 [ arXiv:1302.2924 ] [ INSPIRE ].
87. T. Kobayashi, A Vaidya-type radiating solution in Einstein-Gauss-Bonnet gravity and its application to braneworld, Gen. Rel. Grav. 37 (2005) 1869 [ gr-qc/0504027 ] [ INSPIRE ].
88. H. Maeda, Effects of Gauss-Bonnet terms on final fate of gravitational collapse, Class. Quant. Grav. 23 (2006) 2155 [ gr-qc/0504028 ] [ INSPIRE ].
89. A.E. Dominguez and E. Gallo, Radiating black hole solutions in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 73 (2006) 064018 [ gr-qc/0512150 ] [ INSPIRE ].
90. K. Balasubramanian and J. McGreevy, An analytic Lifshitz black hole, Phys. Rev. D 80 (2009) 104039 [ arXiv:0909.0263 ] [ INSPIRE ].
91. S.N. Solodukhin, Entanglement entropy in non-relativistic field theories, JHEP 04 (2010) 101 [ arXiv:0909.0277 ] [ INSPIRE ].
92. D. Nesterov and S.N. Solodukhin, Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry, Nucl. Phys. B 842 (2011) 141 [ arXiv:1007.1246 ] [ INSPIRE ].
93. S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge U.K. (1973).
94. P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 102 (2009) 211601 [ arXiv:0812.2053 ] [ INSPIRE ].
95. P.M. Chesler and L.G. Yaffe, Boost invariant flow, black hole formation and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 82 (2010) 026006 [ arXiv:0906.4426 ] [ INSPIRE ].
96. P. Figueras, V.E. Hubeny, M. Rangamani and S.F. Ross, Dynamical black holes and expanding plasmas, JHEP 04 (2009) 137 [ arXiv:0902.4696 ] [ INSPIRE ].
97. T. Takayanagi and T. Ugajin, Measuring black hole formations by entanglement entropy via coarse-graining, JHEP 11 (2010) 054 [ arXiv:1008.3439 ] [ INSPIRE ].
98. J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [ INSPIRE ].
99. E. Poisson, A relativist's toolkit, Cambridge University Press, Cambridge U.K. (2004).
100. H. Liu and S.J. Suh, Entanglement tsunami: universal scaling in holographic thermalization, arXiv:1305.7244 [ INSPIRE ].