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Entanglement thermodynamics for charged black holes

Pankaj Chaturvedi*, Vinay Malvimat†, and Gautam Sengupta‡

  • Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India

  • *cpankaj@iitk.ac.in
  • †vinaymm@iitk.ac.in
  • ‡sengupta@iitk.ac.in
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Phys. Rev. D 94, 066004 – Published 14 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.066004

Abstract

The holographic quantum entanglement entropy for an infinite strip region of the boundary for the field theory dual to charged black holes in AdS3+1 is investigated. In this framework we elucidate the low and high temperature behavior of the entanglement entropy pertaining to various limits of the black hole charge. In the low temperature regime we establish a first law of entanglement thermodynamics for the boundary field theory.

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References (48)

  1. H. Araki and E. H. Lieb, Entropy inequalities, Commun. Math. Phys. 18, 160 (1970).
  2. P. Calabrese and J. L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. (2004), P06002.
  3. P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42, 504005 (2009).
  4. C. Holzhey, F. Larsen, and F. Wilczek, Geometric and renormalized entropy in conformal field theory, Nucl. Phys. B424, 443 (1994).
  5. C. G. Callan Jr. and F. Wilczek, On geometric entropy, Phys. Lett. B 333, 55 (1994).
  6. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Entanglement in Quantum Critical Phenomena, Phys. Rev. Lett. 90, 227902 (2003).
  7. J. I. Latorre, E. Rico, and G. Vidal, Ground state entanglement in quantum spin chains, Quantum Inf. Comput. 4, 48 (2004).
  8. S. Sotiriadis and J. Cardy, Quantum quench in interacting field theory: A Self-consistent approximation, Phys. Rev. B 81, 134305 (2010).
  9. J. Cardy, Measuring Entanglement Using Quantum Quenches, Phys. Rev. Lett. 106, 150404 (2011).
  10. P. Calabrese, J. Cardy, and E. Tonni, Entanglement Negativity in Quantum Field Theory, Phys. Rev. Lett. 109, 130502 (2012).
  11. P. Calabrese, J. Cardy, and E. Tonni, Finite temperature entanglement negativity in conformal field theory, J. Phys. A 48, 015006 (2015).
  12. J. Cardy, Quantum quenches to a critical point in one dimension: Some further results (unpublished).
  13. M. Cramer and J. Eisert, Correlations, spectral gap and entanglement in harmonic quantum systems on generic lattices, New J. Phys. 8, 71 (2006).
  14. M. Cramer, J. Eisert, M. B. Plenio, and J. Dreißig, Entanglement-area law for general bosonic harmonic lattice systems, Phys. Rev. A 73, 012309 (2006).
  15. M. B. Plenio, J. Eisert, J. Dreißig, and M. Cramer, Entropy, Entanglement, and Area: Analytical Results for Harmonic Lattice Systems, Phys. Rev. Lett. 94, 060503 (2005).
  16. M. Cramer, J. Eisert, and M. B. Plenio, Statistics Dependence of the Entanglement Entropy, Phys. Rev. Lett. 98, 220603 (2007).
  17. D. Gioev and I. Klich, Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture, Phys. Rev. Lett. 96, 100503 (2006).
  18. M. M. Wolf, Violation of the Entropic Area Law for Fermions, Phys. Rev. Lett. 96, 010404 (2006).
  19. J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38, 1113 (1999).
  20. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428, 105 (1998).
  21. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998).
  22. E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2, 505 (1998).
  23. O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri, and Y. Oz, Large N field theories, string theory and gravity, Phys. Rep. 323, 183 (2000).
  24. S. Ryu and T. Takayanagi, Holographic Derivation of Entanglement Entropy from AdS/CFT, Phys. Rev. Lett. 96, 181602 (2006).
  25. S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, J. High Energy Phys. 08 (2006) 045.
  26. V. E. Hubeny, M. Rangamani, and T. Takayanagi, A covariant holographic entanglement entropy proposal, J. High Energy Phys. 07 (2007) 062.
  27. T. Nishioka, S. Ryu, and T. Takayanagi, Holographic entanglement entropy: An overview, J. Phys. A 42, 504008 (2009).
  28. M. Headrick and T. Takayanagi, Holographic proof of the strong subadditivity of entanglement entropy, Phys. Rev. D 76, 106013 (2007).
  29. R. Callan, J.-Y. He, and M. Headrick, Strong subadditivity and the covariant holographic entanglement entropy formula, J. High Energy Phys. 06 (2012) 081.
  30. A. C. Wall, Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy, Classical Quantum Gravity 31, 225007 (2014).
  31. E. Caceres, A. Kundu, J. F. Pedraza, and W. Tangarife, Strong subadditivity, null energy condition and charged black holes, J. High Energy Phys. 01 (2014) 084.
  32. B. Chen and J. Long, Strong subadditivity and emergent surface, Phys. Rev. D 90, 066012 (2014).
  33. N. Lashkari, C. Rabideau, P. Sabella-Garnier, and M. Van Raamsdonk, Inviolable energy conditions from entanglement inequalities, J. High Energy Phys. 06 (2015) 067.
  34. M. Cadoni and M. Melis, Holographic entanglement entropy of the BTZ black hole, Found. Phys. 40, 638 (2010).
  35. M. Cadoni and M. Melis, Entanglement entropy of AdS black holes, Entropy 12, 2244 (2010).
  36. V. E. Hubeny, Extremal surfaces as bulk probes in AdS/CFT, J. High Energy Phys. 07 (2012) 093.
  37. W. Fischler and S. Kundu, Strongly coupled gauge theories: High and low temperature behavior of non-local observables, J. High Energy Phys. 05 (2013) 098.
  38. J. Bhattacharya, M. Nozaki, T. Takayanagi, and T. Ugajin, Thermodynamical Property of Entanglement Entropy for Excited States, Phys. Rev. Lett. 110, 091602 (2013).
  39. D. Allahbakhshi, M. Alishahiha, and A. Naseh, Entanglement Thermodynamics, J. High Energy Phys. 08 (2013) 102.
  40. E. Tonni, Holographic entanglement entropy: Near horizon geometry and disconnected regions, J. High Energy Phys. 05 (2011) 004.
  41. P. Caputa, G. Mandal, and R. Sinha, Dynamical entanglement entropy with angular momentum and U(1) charge, J. High Energy Phys. 11 (2013) 052.
  42. S. A. H. Mansoori, B. Mirza, M. D. Darareh, and S. Janbaz, Entanglement thermodynamics of the generalized charged BTZ black hole (unpublished).
  43. P. Caputa, V. Jejjala, and H. Soltanpanahi, Entanglement entropy of extremal BTZ black holes, Phys. Rev. D 89, 046006 (2014).
  44. D. D. Blanco, H. Casini, L.-Y. Hung, and R. C. Myers, Relative entropy and holography, J. High Energy Phys. 08 (2013) 060.
  45. C. Park, Holographic entanglement entropy in the nonconformal medium, Phys. Rev. D 91, 126003 (2015).
  46. S. He, J.-R. Sun, and H.-Q. Zhang, On holographic entanglement entropy with second order excitations (unpublished).
  47. V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208, 413 (1999).
  48. A. Dey, S. Mahapatra, and T. Sarkar, Very general holographic superconductors and entanglement thermodynamics, J. High Energy Phys. 12 (2014) 135.

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Phys. Rev. D 94, 066004– Published 14 September, 2016
  • Received 1 August 2016

© 2016 American Physical Society

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