Abstract
We present the results of our studies of the entanglement entropy of a super- conducting system described holographically as a fully back-reacted gravity system, with a stable ground state. We use the holographic prescription for the entanglement entropy. We uncover the behavior of the entropy across the superconducting phase transition, showing the reorganization of the degrees of freedom of the system. We exhibit the behaviour of the entanglement entropy from the superconducting transition all the way down to the ground state at T = 0. In some cases, we also observe a novel transition in the entanglement entropy at intermediate temperatures, resulting from the detection of an additional length scale.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
S.N. Solodukhin, Entanglement entropy of black holes and AdS/CFT correspondence, Phys. Rev. Lett. 97 (2006) 201601 [hep-th/0606205] [INSPIRE].
T. Hirata and T. Takayanagi, AdS/CFT and strong subadditivity of entanglement entropy, JHEP 02 (2007) 042 [hep-th/0608213] [INSPIRE].
T. Nishioka and T. Takayanagi, AdS Bubbles, entropy and closed string tachyons, JHEP 01 (2007) 090 [hep-th/0611035] [INSPIRE].
M. Headrick and T. Takayanagi, A holographic proof of the strong subadditivity of entanglement entropy, Phys. Rev. D 76 (2007) 106013 [arXiv:0704.3719] [INSPIRE].
S.N. Solodukhin, Entanglement entropy, conformal invariance and extrinsic geometry, Phys. Lett. B 665 (2008) 305 [arXiv:0802.3117] [INSPIRE].
H. Casini, M. Huerta and L. Leitao, Entanglement entropy for a Dirac fermion in three dimensions: Vertex contribution, Nucl. Phys. B 814 (2009) 594 [arXiv:0811.1968] [INSPIRE].
T. Nishioka, S. Ryu and T. Takayanagi, Holographic entanglement entropy: an overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
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) 1133] [hep-th/9711200] [INSPIRE].
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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [INSPIRE].
S.S. Gubser and I. Mitra, Instability of charged black holes in Anti-de Sitter space, hep-th/0009126 [INSPIRE].
N. Bobev, N. Halmagyi, K. Pilch and N.P. Warner, Supergravity instabilities of non-supersymmetric quantum critical points, Class. Quant. Grav. 27 (2010) 235013 [arXiv:1006.2546] [INSPIRE].
D. Cassani and P. Koerber, Tri-Sasakian consistent reduction, JHEP 01 (2012) 086 [arXiv:1110.5327] [INSPIRE].
N. Bobev, A. Kundu, K. Pilch and N.P. Warner, Minimal holographic superconductors from maximal supergravity, JHEP 03 (2012) 064 [arXiv:1110.3454] [INSPIRE].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
P. Basu, A. Mukherjee and H.-H. Shieh, Supercurrent: Vector Hair for an AdS Black Hole, Phys. Rev. D 79 (2009) 045010 [arXiv:0809.4494] [INSPIRE].
C. Herzog, P. Kovtun and D. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [INSPIRE].
T. Albash and C.V. Johnson, Holographic entanglement entropy and renormalization group flow, JHEP 02 (2012) 095 [arXiv:1110.1074] [INSPIRE].
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].
V. Balasubramanian et al., Holographic thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
R.C. Myers and A. Singh, Comments on holographic entanglement entropy and RG flows, JHEP 04 (2012) 122 [arXiv:1202.2068] [INSPIRE].
I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140] [INSPIRE].
A. Pakman and A. Parnachev, Topological entanglement entropy and holography, JHEP 07 (2008) 097 [arXiv:0805.1891] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1202.2605
Rights and permissions
About this article
Cite this article
Albash, T., Johnson, C.V. Holographic studies of entanglement entropy in superconductors. J. High Energ. Phys. 2012, 79 (2012). https://doi.org/10.1007/JHEP05(2012)079
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2012)079