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Mutual information and holographic entanglement entropy for strongly coupled R-charged plasmas

Gustavo de Oliveira1,*, Ronaldo F. Costa1,†, Lucas C. Céleri2,‡, and Romulo Rougemont1,§

  • *Contact author: gustav.o.liveira@discente.ufg.br
  • †Contact author: ronaldo_costa@discente.ufg.br
  • ‡Contact author: lucas@qpequi.com
  • §Contact author: rougemont@ufg.br
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Phys. Rev. D 112, 066010 – Published 17 September, 2025

DOI: https://doi.org/10.1103/ylpl-96p1

Abstract

We numerically evaluate, for slab entangling geometries, the mutual information and the holographic entanglement entropy between strongly interacting fields in different spatial regions for two different conformal holographic models at finite temperature and R-charge density. The 1R-Charge Black Hole (1RCBH) model describes a strongly interacting fluid with a critical point in its phase diagram, while the 2R-Charge Black Hole model has no critical point. In both models, we find that the mutual information tends to be overall reduced by increasing the value of μ/T at larger values of the separation length x between two disjoint spatial regions of the medium, while the opposite tendency is observed at lower values of x. We also observe that, very close to the critical point of the 1RCBH model, the mutual information tends to increase with increasing μ/T in the stable branch of black hole solutions. Moreover, the mutual information between the fields in the two disjoint regions is observed to be enhanced by increasing the characteristic size ℓ of these regions, with such an enhancement asymptotically saturating, thus suggesting the existence of a finite field correlation length between the disjoint regions of the system. The finite part of the entanglement entropy may change sign depending on the values of μ/T and ℓ, and it correctly detects the critical point of the 1RCBH model, a feature that is also adequately detected by the mutual information.

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References (76)

  1. J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998).
  2. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998).
  3. E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998).
  4. E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998).
  5. J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973).
  6. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975); 46, 206(E) (1976).
  7. M. Natsuume, AdS/CFT Duality User Guide (Springer, 2015), Vol. 903, 10.1007/978-4-431-55441-7; arXiv:1409.3575.
  8. S. Kundu and J. F. Pedraza, J. High Energy Phys. 08 (2016) 177.
  9. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2012).
  10. V. Vedral, Rev. Mod. Phys. 74, 197 (2002).
  11. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
  12. S. Ryu and T. Takayanagi, Phys. Rev. Lett. 96, 181602 (2006).
  13. S. Ryu and T. Takayanagi, J. High Energy Phys. 08 (2006) 045.
  14. V. E. Hubeny, M. Rangamani, and T. Takayanagi, J. High Energy Phys. 07 (2007) 062.
  15. A. Lewkowycz and J. Maldacena, J. High Energy Phys. 08 (2013) 090.
  16. X. Dong, A. Lewkowycz, and M. Rangamani, J. High Energy Phys. 11 (2016) 028.
  17. T. Nishioka, S. Ryu, and T. Takayanagi, J. Phys. A 42, 504008 (2009).
  18. M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy (Springer, New York, 2017), Vol. 931.
  19. T. Nishioka, Rev. Mod. Phys. 90, 035007 (2018).
  20. O. DeWolfe, S. S. Gubser, and C. Rosen, Phys. Rev. D 84, 126014 (2011).
  21. O. DeWolfe, S. S. Gubser, and C. Rosen, Phys. Rev. D 86, 106002 (2012).
  22. S. I. Finazzo, R. Rougemont, M. Zaniboni, R. Critelli, and J. Noronha, J. High Energy Phys. 01 (2017) 137.
  23. G. de Oliveira and R. Rougemont, J. High Energy Phys. 11 (2024) 079.
  24. K. Behrndt, M. Cvetic, and W. A. Sabra, Nucl. Phys. B553, 317 (1999).
  25. M. Cvetic and S. S. Gubser, J. High Energy Phys. 04 (1999) 024.
  26. M. Asadi, H. Soltanpanahi, and F. Taghinavaz, J. High Energy Phys. 05 (2021) 287.
  27. R. Critelli, R. Rougemont, and J. Noronha, J. High Energy Phys. 12 (2017) 029.
  28. R. Critelli, R. Rougemont, and J. Noronha, Phys. Rev. D 99, 066004 (2019).
  29. R. Rougemont and W. Barreto, Phys. Rev. D 106, 126023 (2022).
  30. R. Rougemont and W. Barreto, Phys. Rev. D 109, 126009 (2024).
  31. H. Ebrahim, M. Asadi, and M. Ali-Akbari, J. High Energy Phys. 09 (2019) 023.
  32. H. Ebrahim and G.-M. Nafisi, Phys. Rev. D 102, 106007 (2020).
  33. B. Amrahi, M. Ali-Akbari, and M. Asadi, Phys. Rev. D 103, 086019 (2021).
  34. D. Karan and S. Pant, Eur. Phys. J. C 84, 113 (2024).
  35. B. Amrahi, M. Asadi, and F. Taghinavaz, Eur. Phys. J. C 84, 505 (2024).
  36. O. Henriksson, C. Hoyos, and N. Jokela, J. High Energy Phys. 09 (2019) 088.
  37. O. J. C. Dias, P. Mitra, and J. E. Santos, J. High Energy Phys. 05 (2023) 053.
  38. L. Gladden, V. Ivo, P. Kovtun, and A. O. Starinets, Phys. Rev. D 111, 086030 (2025).
  39. A. Anabalon and J. Oliva, Phys. Rev. Lett. 133, 121601 (2024).
  40. A. Buchel, arXiv:2501.01856.
  41. A. Buchel, arXiv:2501.12403.
  42. A. Anabalón, M. Chernicoff, G. Giribet, J. Oliva, and M. Reyes, arXiv:2501.15533.
  43. A. Buchel, arXiv:2502.11354.
  44. J. W. York, Jr., Phys. Rev. Lett. 28, 1082 (1972).
  45. G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2752 (1977).
  46. E. Poisson, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics (Cambridge University Press, Cambridge, England, 2009).
  47. M. Bianchi, D. Z. Freedman, and K. Skenderis, Nucl. Phys. B631, 159 (2002).
  48. K. Skenderis, Classical Quantum Gravity 19, 5849 (2002).
  49. S. de Haro, S. N. Solodukhin, and K. Skenderis, Commun. Math. Phys. 217, 595 (2001).
  50. I. Papadimitriou, J. High Energy Phys. 08 (2011) 119.
  51. J. Lindgren, I. Papadimitriou, A. Taliotis, and J. Vanhoof, J. High Energy Phys. 07 (2015) 094.
  52. H. Elvang and M. Hadjiantonis, J. High Energy Phys. 06 (2016) 046.
  53. P. Breitenlohner and D. Z. Freedman, Ann. Phys. (N.Y.) 144, 249 (1982).
  54. P. Breitenlohner and D. Z. Freedman, Phys. Lett. 115B, 197 (1982).
  55. O. DeWolfe, S. S. Gubser, and C. Rosen, Phys. Rev. D 83, 086005 (2011).
  56. S. S. Gubser, I. R. Klebanov, and A. W. Peet, Phys. Rev. D 54, 3915 (1996).
  57. R. C. Myers and O. Tafjord, J. High Energy Phys. 11 (2001) 009.
  58. P. Calabrese and J. L. Cardy, J. Stat. Mech. (2004) P06002.
  59. J. Eisert, M. Cramer, and M. B. Plenio, Rev. Mod. Phys. 82, 277 (2010).
  60. M. Levin and X.-G. Wen, Phys. Rev. Lett. 96, 110405 (2006).
  61. A. Kitaev and J. Preskill, Phys. Rev. Lett. 96, 110404 (2006).
  62. N. Laflorencie, Phys. Rep. 646, 1 (2016).
  63. M. Van Raamsdonk, Gen. Relativ. Gravit. 42, 2323 (2010).
  64. H. Casini, M. Huerta, and R. C. Myers, J. High Energy Phys. 05 (2011) 036.
  65. S. N. Solodukhin, Living Rev. Relativity 14, 8 (2011).
  66. X. Dong, J. High Energy Phys. 01 (2014) 044.
  67. T. Faulkner, A. Lewkowycz, and J. Maldacena, J. High Energy Phys. 11 (2013) 074.
  68. W. Fischler and S. Kundu, J. High Energy Phys. 05 (2013) 098.
  69. E. Quijada and H. Boschi-Filho, arXiv:1711.08505.
  70. M. L. Bellac, Thermal Field Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2011).
  71. A. K. Das, Finite Temperature Field Theory (World Scientific, New York, 1997).
  72. E. Tonni, J. High Energy Phys. 05 (2011) 004.
  73. W. Fischler, A. Kundu, and S. Kundu, Phys. Rev. D 87, 126012 (2013).
  74. I. Wolfram Research, Mathematica, Version 14.0, Champaign, IL (2024), available at https://www.wolfram.com/mathematica.
  75. Domen, Answer to: How to get negative values of function on y axis, when i am plotting as logplot [duplicate] (2021), mathematica Stack Exchange, Accessed: 2025-03-08.
  76. Edmund, Answer to: ’symlog’-like plot with a mixed log-linear-log scale (2020), mathematica Stack Exchange, Accessed: 2025-03-08.

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Phys. Rev. D 112, 066010– Published 17 September, 2025
  • Received 21 May 2025
  • Accepted 4 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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