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Holographic transport and density waves

  • Aristomenis DonosEmail author
  • Christiana Pantelidou
Open Access
Regular Article - Theoretical Physics
  • 23 Downloads

Abstract

We consider transport of heat and charge in holographic lattices which are phases of strongly coupled matter in which translations are broken explicitly. In these systems, we study a spontaneous density wave that breaks translations incommensurately to the lattice. The emergent gapless mode due to symmetry breaking couples to the heat current impacting transport at low frequencies. We study the effects of this coupling when the mode is freely sliding as well as after the introduction of a small deformation parameter which pins down the density wave. We prove that the DC transport coefficients are discontinuous in the limit of the pinning parameter going to zero. From the perspective of finite frequency thermoelectric conductivity, this limiting process is accompanied by the transfer of spectral weight to frequencies set by the pinning parameter. As expected, for weak momentum relaxation, this spectral weight transfer appears as a shift of the Drude peak.

Keywords

AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
  2. [2]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
  4. [4]
    S.A. Hartnoll and D.M. Hofman, Locally critical resistivities from Umklapp scattering, Phys. Rev. Lett. 108 (2012) 241601 [arXiv:1201.3917] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    P. Chesler, A. Lucas and S. Sachdev, Conformal field theories in a periodic potential: results from holography and field theory, Phys. Rev. D 89 (2014) 026005 [arXiv:1308.0329] [INSPIRE].
  7. [7]
    A. Donos and J.P. Gauntlett, The thermoelectric properties of inhomogeneous holographic lattices, JHEP 01 (2015) 035 [arXiv:1409.6875] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
  12. [12]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
  13. [13]
    S. Nakamura, H. Ooguri and C.-S. Park, Gravity dual of spatially modulated phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].
  14. [14]
    A. Donos and J.P. Gauntlett, Black holes dual to helical current phases, Phys. Rev. D 86 (2012) 064010 [arXiv:1204.1734] [INSPIRE].
  15. [15]
    A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  16. [16]
    A. Donos and J.P. Gauntlett, Holographic charge density waves, Phys. Rev. D 87 (2013) 126008 [arXiv:1303.4398] [INSPIRE].
  17. [17]
    B. Withers, Holographic checkerboards, JHEP 09 (2014) 102 [arXiv:1407.1085] [INSPIRE].
  18. [18]
    A. Donos and J.P. Gauntlett, Minimally packed phases in holography, JHEP 03 (2016) 148 [arXiv:1512.06861] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    A. Amoretti, D. Areán, B. Goutéraux and D. Musso, Effective holographic theory of charge density waves, Phys. Rev. D 97 (2018) 086017 [arXiv:1711.06610] [INSPIRE].
  20. [20]
    A. Amoretti, D. Areán, B. Goutéraux and D. Musso, DC resistivity of quantum critical, charge density wave states from gauge-gravity duality, Phys. Rev. Lett. 120 (2018) 171603 [arXiv:1712.07994] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    A. Donos, J.P. Gauntlett, T. Griffin and V. Ziogas, Incoherent transport for phases that spontaneously break translations, JHEP 04 (2018) 053 [arXiv:1801.09084] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    B. Goutéraux, N. Jokela and A. Pönni, Incoherent conductivity of holographic charge density waves, JHEP 07 (2018) 004 [arXiv:1803.03089] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    T. Andrade, A. Krikun, K. Schalm and J. Zaanen, Doping the holographic Mott insulator, Nature Phys. 14 (2018) 1049 [arXiv:1710.05791] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    T. Andrade and A. Krikun, Commensurate lock-in in holographic non-homogeneous lattices, JHEP 03 (2017) 168 [arXiv:1701.04625] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    T. Andrade, M. Baggioli, A. Krikun and N. Poovuttikul, Pinning of longitudinal phonons in holographic spontaneous helices, JHEP 02 (2018) 085 [arXiv:1708.08306] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  26. [26]
    T. Andrade and A. Krikun, Commensurability effects in holographic homogeneous lattices, JHEP 05 (2016) 039 [arXiv:1512.02465] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    A. Amoretti, D. Areán, B. Goutéraux and D. Musso, A holographic strange metal with slowly fluctuating translational order, arXiv:1812.08118 [INSPIRE].
  28. [28]
    T. Andrade and A. Krikun, Coherent vs. incoherent transport in holographic strange insulators, arXiv:1812.08132 [INSPIRE].
  29. [29]
    L. Alberte et al., Holographic phonons, Phys. Rev. Lett. 120 (2018) 171602 [arXiv:1711.03100] [INSPIRE].
  30. [30]
    L. Alberte et al., Black hole elasticity and gapped transverse phonons in holography, JHEP 01 (2018) 129 [arXiv:1708.08477] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    G. Policastro, D.T. Son and A.O. Starinets, The Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].
  32. [32]
    N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].
  33. [33]
    M. Blake and D. Tong, Universal resistivity from holographic massive gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].
  34. [34]
    A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    A. Donos and J.P. Gauntlett, Navier-Stokes equations on black hole horizons and DC thermoelectric conductivity, Phys. Rev. D 92 (2015) 121901 [arXiv:1506.01360] [INSPIRE].
  36. [36]
    E. Banks, A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities and Stokes flows on black hole horizons, JHEP 10 (2015) 103 [arXiv:1507.00234] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    G. Grüner, The dynamics of charge-density waves, Rev. Mod. Phys. 60 (1988) 1129.Google Scholar
  38. [38]
    L.V. Delacrétaz, B. Goutéraux, S.A. Hartnoll and A. Karlsson, Bad metals from fluctuating density waves, SciPost Phys. 3 (2017) 025 [arXiv:1612.04381] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    A. Donos, J.P. Gauntlett, T. Griffin and L. Melgar, DC Conductivity and Higher Derivative Gravity, Class. Quant. Grav. 34 (2017) 135015 [arXiv:1701.01389] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    A. Donos, D. Martin and C. Pantelidou, Sliding density waves and the Hall angle, work in progress.Google Scholar
  43. [43]
    M. Blake and A. Donos, Quantum critical transport and the Hall angle, Phys. Rev. Lett. 114 (2015) 021601 [arXiv:1406.1659] [INSPIRE].
  44. [44]
    M. Blake, Magnetotransport from the fluid/gravity correspondence, JHEP 10 (2015) 078 [arXiv:1507.04870] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    A. Donos, J.P. Gauntlett, T. Griffin and L. Melgar, DC conductivity of magnetised holographic matter, JHEP 01 (2016) 113 [arXiv:1511.00713] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Centre for Particle Theory and Department of Mathematical SciencesDurham UniversityDurhamU.K.

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