Skip to main content
SpringerLink
Log in

Holographic lattice in Einstein-Maxwell-dilaton gravity

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We construct an ionic lattice background in the framework of Einstein-Maxwell-dilaton theory in four dimensional space time. The optical conductivity of the dual field theory on the boundary is investigated. Due to the lattice effects, we find the imaginary part of the conductivity is manifestly suppressed in the zero frequency limit, while the DC conductivity approaches a finite value such that the previous delta function reflecting the translation symmetry is absent. Such a behavior can be exactly fit by the Drude law at low frequency. Moreover, we find that the modulus of the optical conductivity exhibits a power-law behavior at intermediate frequency regime. Our results provides further support for the universality of such power-law behavior recently disclosed in Einstein-Maxwell theory by Horowitz, Santos and Tong.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    Google Scholar 

  3. J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].

    Google Scholar 

  4. S. Sachdev, Condensed matter and AdS/CFT, Lect. Notes Phys. 828 (2011) 273 [arXiv:1002.2947] [INSPIRE].

    Article  ADS  Google Scholar 

  5. S.A. Hartnoll, Horizons, holography and condensed matter, arXiv:1106.4324 [INSPIRE].

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

    Article  MathSciNet  ADS  Google Scholar 

  7. G.T. Horowitz, J.E. Santos and D. Tong, Further evidence for lattice-induced scaling, JHEP 11 (2012) 102 [arXiv:1209.1098] [INSPIRE].

    Article  ADS  Google Scholar 

  8. G.T. Horowitz and J.E. Santos, General relativity and the cuprates, arXiv:1302.6586 [INSPIRE].

  9. 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 

  10. Y. Ling, C. Niu, J.-P. Wu, Z.-Y. Xian and H.-B. Zhang, Holographic Fermionic liquid with lattices, JHEP 07 (2013) 045 [arXiv:1304.2128] [INSPIRE].

    Article  ADS  Google Scholar 

  11. 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 

  12. A. Donos and S.A. Hartnoll, Metal-insulator transition in holography, arXiv:1212.2998 [INSPIRE].

  13. N. Iizuka and K. Maeda, Towards the lattice effects on the holographic superconductor, JHEP 11 (2012) 117 [arXiv:1207.2943] [INSPIRE].

    Article  ADS  Google Scholar 

  14. 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 

  15. 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 

  16. 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 

  17. N. Bao, S. Harrison, S. Kachru and S. Sachdev, Vortex lattices and crystalline geometries, Phys. Rev. D 88 (2013) 026002 [arXiv:1303.4390] [INSPIRE].

    ADS  Google Scholar 

  18. M.R.M. Mozaffar and A. Mollabashi, Crystalline geometries from Fermionic vortex lattice, arXiv:1307.7397 [INSPIRE].

  19. K. Wong, A non-Abelian vortex lattice in strongly coupled systems, JHEP 10 (2013) 148 [arXiv:1307.7839] [INSPIRE].

    Article  ADS  Google Scholar 

  20. M.R.M. Mozaffar and A. Mollabashi, Crystalline geometries from Fermionic vortex lattice, arXiv:1307.7397 [INSPIRE].

  21. P. Chesler, A. Lucas and S. Sachdev, Conformal field theories in a periodic potential: results from holography and field theory, arXiv:1308.0329 [INSPIRE].

  22. D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].

  23. R.A. Davison, Momentum relaxation in holographic massive gravity, arXiv:1306.5792 [INSPIRE].

  24. M. Blake and D. Tong, Universal resistivity from holographic massive gravity, arXiv:1308.4970 [INSPIRE].

  25. D. van der Marel et al., Power-law optical conductivity with a constant phase angle in high T c superconductors, Nature 425 (2003) 271 [cond-mat/0309172].

    Article  ADS  Google Scholar 

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

  27. S.S. Gubser and F.D. Rocha, Peculiar properties of a charged dilatonic black hole in AdS 5, Phys. Rev. D 81 (2010) 046001 [arXiv:0911.2898] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  28. M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].

    Article  ADS  Google Scholar 

  29. S.S. Gubser and I. Mitra, The evolution of unstable black holes in anti-de Sitter space, JHEP 08 (2001) 018 [hep-th/0011127] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. M. Cvetič and S.S. Gubser, Thermodynamic stability and phases of general spinning branes, JHEP 07 (1999) 010 [hep-th/9903132] [INSPIRE].

    Article  ADS  Google Scholar 

  31. J.-P. Wu, Some properties of the holographic fermions in an extremal charged dilatonic black hole, Phys. Rev. D 84 (2011) 064008 [arXiv:1108.6134] [INSPIRE].

    ADS  Google Scholar 

  32. S.S. Gubser and J. Ren, Analytic fermionic Green’s functions from holography, Phys. Rev. D 86 (2012) 046004 [arXiv:1204.6315] [INSPIRE].

    ADS  Google Scholar 

  33. W.-J. Li, R. Meyer and H.-B. Zhang, Holographic non-relativistic fermionic fixed point by the charged dilatonic black hole, JHEP 01 (2012) 153 [arXiv:1111.3783] [INSPIRE].

    Article  ADS  Google Scholar 

  34. X.-M. Kuang, B. Wang and J.-P. Wu, Dynamical gap from holography in the charged dilaton black hole, Class. Quant. Grav. 30 (2013) 145011 [arXiv:1210.5735] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. 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 

  36. 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 

  37. K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of charged dilaton black holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. M. Cadoni, G. D’Appollonio and P. Pani, Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime, JHEP 03 (2010) 100 [arXiv:0912.3520] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. A. Salvio, Holographic superfluids and superconductors in dilaton-gravity, JHEP 09 (2012) 134 [arXiv:1207.3800] [INSPIRE].

    Article  ADS  Google Scholar 

  40. A. Salvio, Transitions in dilaton holography with global or local symmetries, JHEP 03 (2013) 136 [arXiv:1302.4898] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. 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 

  42. T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China

    Yi Ling, Chao Niu & Zhuo-Yu Xian

  2. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Yi Ling

  3. Department of Physics, School of Mathematics and Physics, Bohai University, Jinzhou, 121013, China

    Jian-Pin Wu

  4. Department of Physics, Hanyang University, Seoul, 133-791, Korea

    Jian-Pin Wu

  5. Center for Quantum Spacetime, Sogang University, Seoul, 121-742, Korea

    Jian-Pin Wu

Authors
  1. Yi Ling
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chao Niu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jian-Pin Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhuo-Yu Xian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chao Niu.

Additional information

ArXiv ePrint: 1309.4580

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ling, Y., Niu, C., Wu, JP. et al. Holographic lattice in Einstein-Maxwell-dilaton gravity. J. High Energ. Phys. 2013, 6 (2013). https://doi.org/10.1007/JHEP11(2013)006

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2013)006

Keywords

Search

Navigation