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Further evidence for lattice-induced scaling

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Abstract

We continue our study of holographic transport in the presence of a background lattice. We recently found evidence that the presence of a lattice induces a new intermediate scaling regime in asymptotically AdS 4 spacetimes. This manifests itself in the optical conductivity which exhibits a robust power-law dependence on frequency, σ ∼ ω −2/3, in a “mid-infrared” regime, a result which is in striking agreement with experiments on the cuprates. Here we provide further evidence for the existence of this intermediate scaling regime. We demonstrate similar scaling in the thermoelectric conductivity, find analogous scalings in asymptotically AdS 5 spacetimes, and show that we get the same results with an ionic lattice.

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References

  1. G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].

    Article  ADS  Google Scholar 

  2. S.A. Hartnoll and D.M. Hofman, Locally critical resistivities from umklapp scattering, Phys. Rev. Lett. 108 (2012) 241601 [arXiv:1201.3917] [INSPIRE].

    Article  ADS  Google Scholar 

  3. K. Maeda, T. Okamura and J.-I. Koga, Inhomogeneous charged black hole solutions in asymptotically anti-de Sitter spacetime, Phys. Rev. D 85 (2012) 066003 [arXiv:1107.3677] [INSPIRE].

    ADS  Google Scholar 

  4. N. Iizuka and K. Maeda, Towards the lattice effects on the holographic superconductor, arXiv:1207.2943 [INSPIRE].

  5. Y. Liu, K. Schalm, Y.-W. Sun and J. Zaanen, Lattice potentials and fermions in holographic non Fermi-liquids: hybridizing local quantum criticality, JHEP 10 (2012) 036 [arXiv:1205.5227] [INSPIRE].

    Article  ADS  Google Scholar 

  6. A. Donos and S.A. Hartnoll, Universal linear in temperature resistivity from black hole superradiance, arXiv:1208.4102 [INSPIRE].

  7. S. Kachru, A. Karch and S. Yaida, Holographic lattices, dimers and glasses, Phys. Rev. D 81 (2010) 026007 [arXiv:0909.2639] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  8. S. Kachru, A. Karch and S. Yaida, Adventures in holographic dimer models, New J. Phys. 13 (2011) 035004 [arXiv:1009.3268] [INSPIRE].

    Article  ADS  Google Scholar 

  9. K. Jensen, S. Kachru, A. Karch, J. Polchinski and E. Silverstein, Towards a holographic marginal Fermi liquid, Phys. Rev. D 84 (2011) 126002 [arXiv:1105.1772] [INSPIRE].

    ADS  Google Scholar 

  10. S. Nakamura, H. Ooguri and C.-S. Park, Gravity dual of spatially modulated phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].

    ADS  Google Scholar 

  11. H. Ooguri and C.-S. Park, Holographic end-point of spatially modulated phase transition, Phys. Rev. D 82 (2010) 126001 [arXiv:1007.3737] [INSPIRE].

    ADS  Google Scholar 

  12. S. Bolognesi and D. Tong, Monopoles and holography, JHEP 01 (2011) 153 [arXiv:1010.4178] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [INSPIRE].

    Article  ADS  Google Scholar 

  14. A. Donos and J.P. Gauntlett, Holographic helical superconductors, JHEP 12 (2011) 091 [arXiv:1109.3866] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].

    Article  ADS  Google Scholar 

  16. A. Donos and J.P. Gauntlett, Helical superconducting black holes, Phys. Rev. Lett. 108 (2012) 211601 [arXiv:1203.0533] [INSPIRE].

    Article  ADS  Google Scholar 

  17. D. van der Marel et al., Quantum critical behaviour in a high T c superconductor, Nature 425 (2003) 271 [arXiv:cond-mat/0309172].

    Article  ADS  Google Scholar 

  18. D. van der Marel, F. Carbone, A.B. Kuzmenko and E. Giannini, Scaling properties of the optical conductivity of Bi-based cuprates, Annals Phys. 321 (2006) 1716 [cond-mat/0604037].

    Article  ADS  Google Scholar 

  19. A. El Azrak et al., Infrared properties of YBa 2 Cu 3 O 7 and Bi 2 Sr 2 Ca n−1 Cu n O 2n+4 thin films, Phys. Rev. B 49 (1994) 9846.

    ADS  Google Scholar 

  20. P.W. Anderson, Infrared conductivity of cuprate metals: detailed fit using luttinger liquid theory, Phys. Rev. B 55 (1997) 11785 [cond-mat/9506140].

    ADS  Google Scholar 

  21. T. Kato and M. Imada, Thermodynamics and optical conductivity of a dissipative carrier in a tight binding model, J. Phys. Soc. Japan 67 (1998) 2828 [cond-mat/9711208].

    Article  ADS  Google Scholar 

  22. M.R. Norman and A.V. Chubukov, High-frequency behavior of the infrared conductivity of cuprates, Phys. Rev. B 73 (2006) 140501 [cond-mat/0511584].

    ADS  Google Scholar 

  23. M. Headrick, S. Kitchen and T. Wiseman, A new approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav. 27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].

    Google Scholar 

  25. V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. S.A. Hartnoll and C.P. Herzog, Ohm’s law at strong coupling: S duality and the cyclotron resonance, Phys. Rev. D 76 (2007) 106012 [arXiv:0706.3228] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  27. M. Taylor, More on counterterms in the gravitational action and anomalies, hep-th/0002125 [INSPIRE].

  28. G.T. Horowitz and M.M. Roberts, Holographic superconductors with various condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].

    ADS  Google Scholar 

  29. R. Flauger, E. Pajer and S. Papanikolaou, A striped holographic superconductor, Phys. Rev. D 83 (2011) 064009 [arXiv:1010.1775] [INSPIRE].

    ADS  Google Scholar 

  30. J.A. Hutasoit, G. Siopsis and J. Therrien, Conductivity of strongly coupled striped superconductor, arXiv:1208.2964 [INSPIRE].

  31. K. Takenaka et al., Coherent-to-incoherent crossover in the optical conductivity of La 2−x Sr x CuO 4 : Charge dynamics of a bad metal, Phys. Rev. B 65 (2002) 092405.

    ADS  Google Scholar 

  32. E. Berti, V. Cardoso and P. Pani, Breit-Wigner resonances and the quasinormal modes of anti-de Sitter black holes, Phys. Rev. D 79 (2009) 101501 [arXiv:0903.5311] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  33. C. Charmousis, B. Gouteraux, B. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].

    Article  ADS  Google Scholar 

  34. N. Iizuka, N. Kundu, P. Narayan and S.P. Trivedi, Holographic Fermi and Non-Fermi Liquids with Transitions in Dilaton Gravity, JHEP 01 (2012) 094 [arXiv:1105.1162] [INSPIRE].

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of California Santa Barbara, Santa Barbara, CA, 93106, USA

    Gary T. Horowitz & Jorge E. Santos

  2. DAMTP, University of Cambridge, Cambridge, CB3 0WA, UK

    David Tong

Authors
  1. Gary T. Horowitz
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  2. Jorge E. Santos
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  3. David Tong
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Correspondence to Jorge E. Santos.

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ArXiv ePrint: 1209.1098

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Horowitz, G.T., Santos, J.E. & Tong, D. Further evidence for lattice-induced scaling. J. High Energ. Phys. 2012, 102 (2012). https://doi.org/10.1007/JHEP11(2012)102

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  • DOI: https://doi.org/10.1007/JHEP11(2012)102

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