Abstract
We study a holographic model where translations are both spontaneously and explicitly broken, leading to the presence of (pseudo)-phonons in the spectrum. The weak explicit breaking is due to two independent mechanisms: a small source for the condensate itself and additional linearly space-dependent marginal operators. The low energy dynamics of the model is described by Wigner crystal hydrodynamics. In absence of a source for the condensate, the phonons remain gapless, but momentum is relaxed. Turning on a source for the condensate damps and pins the phonons. Finally, we verify that the universal relation between the phonon damping rate, mass and diffusivity reported in [1] continues to hold in this model for weak enough explicit breaking.
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References
A. Amoretti, D. Areán, B. Goutéraux and D. Musso, Universal relaxation in a holographic metallic density wave phase, Phys. Rev. Lett.123 (2019) 211602 [arXiv:1812.08118] [INSPIRE].
P.M. Chaikin and T.C. Lubensky, Principles of condensed matter physics, Cambridge University Press, Cambridge, U.K. (1995).
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP07 (2012) 168 [arXiv:1204.0519] [INSPIRE].
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].
S.A. Hartnoll and J.E. Santos, Disordered horizons: holography of randomly disordered fixed points, Phys. Rev. Lett.112 (2014) 231601 [arXiv:1402.0872] [INSPIRE].
A. Donos and J.P. Gauntlett, The thermoelectric properties of inhomogeneous holographic lattices, JHEP01 (2015) 035 [arXiv:1409.6875] [INSPIRE].
A. Donos, J.P. Gauntlett and V. Ziogas, Diffusion for holographic lattices, JHEP03 (2018) 056 [arXiv:1710.04221] [INSPIRE].
A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys.9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
M. Baggioli and O. Pujolàs, Electron-phonon interactions, metal-insulator transitions and holographic massive gravity, Phys. Rev. Lett.114 (2015) 251602 [arXiv:1411.1003] [INSPIRE].
A. Donos, B. Goutéraux and E. Kiritsis, Holographic metals and insulators with helical symmetry, JHEP09 (2014) 038 [arXiv:1406.6351] [INSPIRE].
R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev.D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].
R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP01 (2015) 039 [arXiv:1411.1062] [INSPIRE].
R.A. Davison and B. Goutéraux, Dissecting holographic conductivities, JHEP09 (2015) 090 [arXiv:1505.05092] [INSPIRE].
T. Andrade and A. Krikun, Coherent vs incoherent transport in holographic strange insulators, JHEP05 (2019) 119 [arXiv:1812.08132] [INSPIRE].
D. Musso, Simplest phonons and pseudo-phonons in field theory, Eur. Phys. J.C 79 (2019) 986 [arXiv:1810.01799] [INSPIRE].
D. Musso and D. Naegels, Phonon and shifton from a real modulated scalar, arXiv:1907.04069 [INSPIRE].
L.V. Delacrétaz, B. Goutéraux, S.A. Hartnoll and A. Karlsson, Theory of hydrodynamic transport in fluctuating electronic charge density wave states, Phys. Rev.B 96 (2017) 195128 [arXiv:1702.05104] [INSPIRE].
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].
M. Ammon, M. Baggioli and A. Jiménez-Alba, A unified description of translational symmetry breaking in holography, JHEP09 (2019) 124 [arXiv:1904.05785] [INSPIRE].
M. Baggioli and S. Grieninger, Zoology of solid & fluid holography — Goldstone modes and phase relaxation, JHEP10 (2019) 235 [arXiv:1905.09488] [INSPIRE].
H. Ooguri and C.-S. Park, Holographic end-point of spatially modulated phase transition, Phys. Rev.D 82 (2010) 126001 [arXiv:1007.3737] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP08 (2011) 140 [arXiv:1106.2004] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic charge density waves, Phys. Rev.D 87 (2013) 126008 [arXiv:1303.4398] [INSPIRE].
B. Withers, Black branes dual to striped phases, Class. Quant. Grav.30 (2013) 155025 [arXiv:1304.0129] [INSPIRE].
B. Withers, Holographic checkerboards, JHEP09 (2014) 102 [arXiv:1407.1085] [INSPIRE].
Y. Ling, C. Niu, J. Wu, Z. Xian and H.-B. Zhang, Metal-insulator transition by holographic charge density waves, Phys. Rev. Lett.113 (2014) 091602 [arXiv:1404.0777] [INSPIRE].
N. Jokela, M. Jarvinen and M. Lippert, Gravity dual of spin and charge density waves, JHEP12 (2014) 083 [arXiv:1408.1397] [INSPIRE].
S. Cremonini, L. Li and J. Ren, Holographic pair and charge density waves, Phys. Rev.D 95 (2017) 041901 [arXiv:1612.04385] [INSPIRE].
R.-G. Cai, L. Li, Y.-Q. Wang and J. Zaanen, Intertwined order and holography: the case of parity breaking pair density waves, Phys. Rev. Lett.119 (2017) 181601 [arXiv:1706.01470] [INSPIRE].
T. Andrade, A. Krikun, K. Schalm and J. Zaanen, Doping the holographic Mott insulator, Nature Phys.14 (2018) 1049 [arXiv:1710.05791] [INSPIRE].
A. Donos and J.P. Gauntlett, Black holes dual to helical current phases, Phys. Rev.D 86 (2012) 064010 [arXiv:1204.1734] [INSPIRE].
A. Amoretti, D. Areán, R. Argurio, D. Musso and L.A. Pando Zayas, A holographic perspective on phonons and pseudo-phonons, JHEP05 (2017) 051 [arXiv:1611.09344] [INSPIRE].
L. Alberte, M. Ammon, A. Jiménez-Alba, M. Baggioli and O. Pujolàs, Holographic phonons, Phys. Rev. Lett.120 (2018) 171602 [arXiv:1711.03100] [INSPIRE].
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].
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].
N. Jokela, M. Jarvinen and M. Lippert, Pinning of holographic sliding stripes, Phys. Rev.D 96 (2017) 106017 [arXiv:1708.07837] [INSPIRE].
T. Andrade, M. Baggioli, A. Krikun and N. Poovuttikul, Pinning of longitudinal phonons in holographic spontaneous helices, JHEP02 (2018) 085 [arXiv:1708.08306] [INSPIRE].
L. Alberte, M. Ammon, M. Baggioli, A. Jiménez and O. Pujolàs, Black hole elasticity and gapped transverse phonons in holography, JHEP01 (2018) 129 [arXiv:1708.08477] [INSPIRE].
A. Donos and C. Pantelidou, Holographic transport and density waves, JHEP05 (2019) 079 [arXiv:1903.05114] [INSPIRE].
A. Amoretti, D. Areán, B. Goutéraux and D. Musso, Diffusion and universal relaxation of holographic phonons, JHEP10 (2019) 068 [arXiv:1904.11445] [INSPIRE].
M. Ammon, M. Baggioli, S. Gray and S. Grieninger, Longitudinal sound and diffusion in holographic massive gravity, JHEP10 (2019) 064 [arXiv:1905.09164] [INSPIRE].
A. Donos, D. Martin, C. Pantelidou and V. Ziogas, Incoherent hydrodynamics and density waves, arXiv:1906.03132 [INSPIRE].
J. Armas and A. Jain, Viscoelastic hydrodynamics and holography, arXiv:1908.01175 [INSPIRE].
A. Donos, D. Martin, C. Pantelidou and V. Ziogas, Hydrodynamics of broken global symmetries in the bulk, JHEP10 (2019) 218 [arXiv:1905.00398] [INSPIRE].
A. Donos, Striped phases from holography, JHEP05 (2013) 059 [arXiv:1303.7211] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys.217 (2001) 595 [hep-th/0002230] [INSPIRE].
M. Kaminski, K. Landsteiner, J. Mas, J.P. Shock and J. Tarrio, Holographic operator mixing and quasinormal modes on the brane, JHEP02 (2010) 021 [arXiv:0911.3610] [INSPIRE].
M. Baggioli and A. Buchel, Holographic viscoelastic hydrodynamics, JHEP03 (2019) 146 [arXiv:1805.06756] [INSPIRE].
B. Withers, Short-lived modes from hydrodynamic dispersion relations, JHEP06 (2018) 059 [arXiv:1803.08058] [INSPIRE].
S. Grozdanov, P.K. Kovtun, A.O. Starinets and P. Tadić, Convergence of the gradient expansion in hydrodynamics, Phys. Rev. Lett.122 (2019) 251601 [arXiv:1904.01018] [INSPIRE].
L. Alberte, M. Baggioli, A. Khmelnitsky and O. Pujolàs, Solid holography and massive gravity, JHEP02 (2016) 114 [arXiv:1510.09089] [INSPIRE].
S.A. Hartnoll, D.M. Ramirez and J.E. Santos, Entropy production, viscosity bounds and bumpy black holes, JHEP03 (2016) 170 [arXiv:1601.02757] [INSPIRE].
L. Alberte, M. Baggioli and O. Pujolàs, Viscosity bound violation in holographic solids and the viscoelastic response, JHEP07 (2016) 074 [arXiv:1601.03384] [INSPIRE].
P. Burikham and N. Poovuttikul, Shear viscosity in holography and effective theory of transport without translational symmetry, Phys. Rev.D 94 (2016) 106001 [arXiv:1601.04624] [INSPIRE].
S.A. Hartnoll and D.M. Hofman, Locally critical resistivities from Umklapp scattering, Phys. Rev. Lett.108 (2012) 241601 [arXiv:1201.3917] [INSPIRE].
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Amoretti, A., Areán, D., Goutéraux, B. et al. Gapless and gapped holographic phonons. J. High Energ. Phys. 2020, 58 (2020). https://doi.org/10.1007/JHEP01(2020)058
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DOI: https://doi.org/10.1007/JHEP01(2020)058