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Fluctuations and instabilities of a holographic metal

  • Niko Jokela
  • Matti Järvinen
  • Matthew Lippert
Article

Abstract

We analyze the quasinormal modes of the D2-D8’ model of 2+1-dimensional, strongly-coupled, charged fermions in a background magnetic field and at non-zero density. The model is known to include a quantum Hall phase with integer filling fraction. As expected, we find a hydrodynamical diffusion mode at small momentum and the nonzero-temperature holographic zero sound, which becomes massive above a critical magnetic field. We confirm the previously-known thermodynamic instability. In addition, we discover an instability at low temperature, large mass, and in a charge density and magnetic field range near the quantum Hall phase to an inhomogeneous striped phase.

Keywords

Intersecting branes models Holography and condensed matter physics (AdS/CMT) 

References

  1. [1]
    A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Quantum Hall Effect in a Holographic Model, JHEP 10 (2010) 063 [arXiv:1003.4965] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  4. [4]
    A. Karch and L. Randall, Localized gravity in string theory, Phys. Rev. Lett. 87 (2001) 061601 [hep-th/0105108] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    A. Karch and L. Randall, Open and closed string interpretation of SUSY CFTs on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].MathSciNetADSGoogle Scholar
  7. [7]
    N.R. Constable, J. Erdmenger, Z. Guralnik and I. Kirsch, Intersecting D-3 branes and holography, Phys. Rev. D 68 (2003) 106007 [hep-th/0211222] [INSPIRE].MathSciNetADSGoogle Scholar
  8. [8]
    T. Sakai and J. Sonnenschein, Probing flavored mesons of confining gauge theories by supergravity, JHEP 09 (2003) 047 [hep-th/0305049] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    J. Babington, J. Erdmenger, N.J. Evans, Z. Guralnik and I. Kirsch, Chiral symmetry breaking and pions in nonsupersymmetric gauge/gravity duals, Phys. Rev. D 69 (2004) 066007 [hep-th/0306018] [INSPIRE].MathSciNetADSGoogle Scholar
  10. [10]
    P. Ouyang, Holomorphic D7 branes and flavored N = 1 gauge theories, Nucl. Phys. B 699 (2004) 207 [hep-th/0311084] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Towards a holographic dual of large-N c QCD, JHEP 05 (2004) 041 [hep-th/0311270] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    M. Van Raamsdonk and K. Whyte, Baryon charge from embedding topology and a continuous meson spectrum in a new holographic gauge theory, JHEP 05 (2010) 073 [arXiv:0912.0752] [INSPIRE].CrossRefGoogle Scholar
  13. [13]
    D.K. Hong and H.-U. Yee, Holographic aspects of three dimensional QCD from string theory, JHEP 05 (2010) 036 [Erratum ibid. 1008 (2010) 120] [arXiv:1003.1306] [INSPIRE].
  14. [14]
    S.S. Pal, Quantum phase transition in a Dp-Dq system, Phys. Rev. D 82 (2010) 086013 [arXiv:1006.2444] [INSPIRE].ADSGoogle Scholar
  15. [15]
    K. Jensen, More Holographic Berezinskii-Kosterlitz-Thouless Transitions, Phys. Rev. D 82 (2010) 046005 [arXiv:1006.3066] [INSPIRE].ADSGoogle Scholar
  16. [16]
    E. Conde and A.V. Ramallo, On the gravity dual of Chern-Simons-matter theories with unquenched flavor, JHEP 07 (2011) 099 [arXiv:1105.6045] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    G. Zafrir, Embedding massive flavor in ABJM, JHEP 10 (2012) 056 [arXiv:1202.4295] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    S.K. Domokos, C. Hoyos and J. Sonnenschein, Holographic Josephson Junctions and Berry holonomy from D-branes, JHEP 10 (2012) 073 [arXiv:1207.2182] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    N. Jokela, J. Mas, A.V. Ramallo and D. Zoakos, Thermodynamics of the brane in Chern-Simons matter theories with flavor, arXiv:1211.0630 [INSPIRE].
  20. [20]
    S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    L. Huijse and S. Sachdev, Fermi surfaces and gauge-gravity duality, Phys. Rev. D 84 (2011) 026001 [arXiv:1104.5022] [INSPIRE].ADSGoogle Scholar
  22. [22]
    M. Ammon, J. Erdmenger, S. Lin, S. Muller, A. O’Bannon and J. P. Shock, On Stability and Transport of Cold Holographic Matter, JHEP 09 (2011) 030 [arXiv:1108.1798] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A. Karch, D. Son and A. Starinets, Zero Sound from Holography, arXiv:0806.3796 [INSPIRE].
  24. [24]
    M. Kulaxizi and A. Parnachev, Comments on Fermi Liquid from Holography, Phys. Rev. D 78 (2008) 086004 [arXiv:0808.3953] [INSPIRE].ADSGoogle Scholar
  25. [25]
    M. Goykhman, A. Parnachev and J. Zaanen, Fluctuations in finite density holographic quantum liquids, JHEP 10 (2012) 045 [arXiv:1204.6232] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    D.K. Brattan, R.A. Davison, S.A. Gentle and A. O’Bannon, Collective Excitations of Holographic Quantum Liquids in a Magnetic Field, JHEP 11 (2012) 084 [arXiv:1209.0009] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    V. Puletti, S. Nowling, L. Thorlacius and T. Zingg, Friedel Oscillations in Holographic Metals, JHEP 01 (2012) 073 [arXiv:1110.4601] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    M. Blake, S. Bolognesi, D. Tong and K. Wong, Holographic Dual of the Lowest Landau Level, JHEP 12 (2012) 039 [arXiv:1208.5771] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    N. Jokela, M. Jarvinen and M. Lippert, A holographic quantum Hall model at integer filling, JHEP 05 (2011) 101 [arXiv:1101.3329] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    J.H. Brodie, L. Susskind and N. Toumbas, How Bob Laughlin tamed the giant graviton from Taub-NUT space, JHEP 02 (2001) 003 [hep-th/0010105] [INSPIRE].MathSciNetADSGoogle Scholar
  31. [31]
    O. Bergman, Y. Okawa and J.H. Brodie, The Stringy quantum Hall fluid, JHEP 11 (2001) 019 [hep-th/0107178] [INSPIRE].MathSciNetADSGoogle Scholar
  32. [32]
    S. Hellerman and L. Susskind, Realizing the quantum Hall system in string theory, hep-th/0107200 [INSPIRE].
  33. [33]
    E. Keski-Vakkuri and P. Kraus, Quantum Hall Effect in AdS/CFT, JHEP 09 (2008) 130 [arXiv:0805.4643] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    J.L. Davis, P. Kraus and A. Shah, Gravity Dual of a Quantum Hall Plateau Transition, JHEP 11 (2008) 020 [arXiv:0809.1876] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    J. Alanen, E. Keski-Vakkuri, P. Kraus and V. Suur-Uski, AC Transport at Holographic Quantum Hall Transitions, JHEP 11 (2009) 014 [arXiv:0905.4538] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    S.-J. Rey, String theory on thin semiconductors: Holographic realization of Fermi points and surfaces, Prog. Theor. Phys. Suppl. 177 (2009) 128 [arXiv:0911.5295] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  37. [37]
    R.C. Myers and M.C. Wapler, Transport Properties of Holographic Defects, JHEP 12 (2008) 115 [arXiv:0811.0480] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  38. [38]
    X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    M. Ammon, M. Kaminski and A. Karch, Hyperscaling-Violation on Probe D-branes, JHEP 11 (2012) 028 [arXiv:1207.1726] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    I. Kanitscheider, K. Skenderis and M. Taylor, Precision holography for non-conformal branes, JHEP 09 (2008) 094 [arXiv:0807.3324] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  41. [41]
    N. Jokela, M. Jarvinen and M. Lippert, Fluctuations of a holographic quantum Hall fluid, JHEP 01 (2012) 072 [arXiv:1107.3836] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    K.-Y. Kim and I. Zahed, Baryonic Response of Dense Holographic QCD, JHEP 12 (2008) 075 [arXiv:0811.0184] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    M. Kaminski, K. Landsteiner, J. Mas, J.P. Shock and J. Tarrio, Holographic Operator Mixing and Quasinormal Modes on the Brane, JHEP 02 (2010) 021 [arXiv:0911.3610] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    O. Bergman, N. Jokela, G. Lifschytz and M. Lippert, Striped instability of a holographic Fermi-like liquid, JHEP 10 (2011) 034 [arXiv:1106.3883] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    N. Jokela, G. Lifschytz and M. Lippert, Magnetic effects in a holographic Fermi-like liquid, JHEP 05 (2012) 105 [arXiv:1204.3914] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    R.A. Davison and A.O. Starinets, Holographic zero sound at finite temperature, Phys. Rev. D 85 (2012) 026004 [arXiv:1109.6343] [INSPIRE].ADSGoogle Scholar
  47. [47]
    A. Gorsky and A. Zayakin, Anomalous Zero Sound, arXiv:1206.4725 [INSPIRE].
  48. [48]
    S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].ADSGoogle Scholar
  49. [49]
    H. Ooguri and C.-S. Park, Holographic End-Point of Spatially Modulated Phase Transition, Phys. Rev. D 82 (2010) 126001 [arXiv:1007.3737] [INSPIRE].ADSGoogle Scholar
  50. [50]
    H. Ooguri and C.-S. Park, Spatially Modulated Phase in Holographic quark-gluon Plasma, Phys. Rev. Lett. 106 (2011) 061601 [arXiv:1011.4144] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  51. [51]
    C.B. Bayona, K. Peeters and M. Zamaklar, A Non-homogeneous ground state of the low-temperature Sakai-Sugimoto model, JHEP 06 (2011) 092 [arXiv:1104.2291] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    A. Donos and J.P. Gauntlett, Holographic helical superconductors, JHEP 12 (2011) 091 [arXiv:1109.3866] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  55. [55]
    H. Ooguri and M. Oshikawa, Instability in magnetic materials with dynamical axion field, Phys. Rev. Lett. 108 (2012) 161803 [arXiv:1112.1414] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and Electric AdS Solutions in String- and M-theory, Class. Quant. Grav. 29 (2012) 194006 [arXiv:1112.4195] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  57. [57]
    A. Ballon-Bayona, K. Peeters and M. Zamaklar, A chiral magnetic spiral in the holographic Sakai-Sugimoto model, JHEP 11 (2012) 164 [arXiv:1209.1953] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    O. Bergman, J. Erdmenger and G. Lifschytz, A Review of Magnetic Phenomena in Probe-Brane Holographic Matter, arXiv:1207.5953 [INSPIRE].
  59. [59]
    N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].MathSciNetADSGoogle Scholar
  60. [60]
    A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  61. [61]
    A. O’Bannon, Hall Conductivity of Flavor Fields from AdS/CFT, Phys. Rev. D 76 (2007) 086007 [arXiv:0708.1994] [INSPIRE].ADSGoogle Scholar
  62. [62]
    K.-Y. Kim and D.-W. Pang, Holographic DC conductivities from the open string metric, JHEP 09 (2011) 051 [arXiv:1108.3791] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    A. Karch, M. Kulaxizi and A. Parnachev, Notes on Properties of Holographic Matter, JHEP 11 (2009) 017 [arXiv:0908.3493] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  64. [64]
    T. Faulkner and H. Liu, Condensed matter physics of a strongly coupled gauge theory with quarks: Some novel features of the phase diagram, arXiv:0812.4278 [INSPIRE].
  65. [65]
    I. Amado, M. Kaminski and K. Landsteiner, Hydrodynamics of Holographic Superconductors, JHEP 05 (2009) 021 [arXiv:0903.2209] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  66. [66]
    L.-Y. Hung and A. Sinha, Holographic quantum liquids in 1 + 1 dimensions, JHEP 01 (2010) 114 [arXiv:0909.3526] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    G. Gruner, The dynamics of spin-density waves, Rev. Mod. Phys. 66 (1994) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    G. Gruner, The dynamics of charge-density waves, Rev. Mod. Phys. 60 (1988) 1129 [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    N. Jokela, G. Lifschytz and M. Lippert, Magneto-roton excitation in a holographic quantum Hall fluid, JHEP 02 (2011) 104 [arXiv:1012.1230] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    G. Lifschytz and M. Lippert, Anomalous conductivity in holographic QCD, Phys. Rev. D 80 (2009) 066005 [arXiv:0904.4772] [INSPIRE].ADSGoogle Scholar
  71. [71]
    S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].ADSGoogle Scholar
  72. [72]
    V.G.M. Puletti, S. Nowling, L. Thorlacius and T. Zingg, Holographic metals at finite temperature, JHEP 01 (2011) 117 [arXiv:1011.6261] [INSPIRE].ADSCrossRefGoogle Scholar
  73. [73]
    J.L. Davis, H. Omid and G.W. Semenoff, Holographic Fermionic Fixed Points in D = 3, JHEP 09 (2011) 124 [arXiv:1107.4397] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  74. [74]
    G. Grignani, N. Kim and G.W. Semenoff, D7-anti-D7 bilayer: holographic dynamical symmetry breaking, arXiv:1208.0867 [INSPIRE].
  75. [75]
    H. Omid and G.W. Semenoff, D3-D7 Holographic dual of a perturbed 3D CFT, arXiv:1208.5176 [INSPIRE].
  76. [76]
    C. Kristjansen, G.W. Semenoff and D. Young, Chiral primary one-point functions in the D3-D7 defect conformal field theory, JHEP 01 (2013) 117 [arXiv:1210.7015] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Niko Jokela
    • 1
  • Matti Järvinen
    • 2
  • Matthew Lippert
    • 2
    • 3
  1. 1.Departamento de Física de Partículas, Universidade de Santiago de Compostela, and Instituto Galego de Física de Altas Enerxías (IGFAE)Santiago de CompostelaSpain
  2. 2.Crete Center for Theoretical Physics, Department of PhysicsUniversity of CreteHeraklionGreece
  3. 3.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamNetherlands

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