Amoretti, AndreaAreán Fraga, DanielGoutéraux, BlaiseMusso, Daniele2020-04-142020-04-142019Amoretti, A., Aréan, D., Goutéraux, B. et al. Diffusion and universal relaxation of holographic phonons. J. High Energ. Phys. 2019, 68 (2019). https://doi.org/10.1007/JHEP10(2019)068http://hdl.handle.net/10347/21382In phases where translations are spontaneously broken, new gapless degrees of freedom appear in the low energy spectrum (the phonons). At long wavelengths, they couple to small fluctuations of the conserved densities of the system. This mixing is captured by new diffusive transport coefficients, as well as qualitatively different collective modes, such as shear sound modes. We use Gauge/Gravity duality to model such phases and analytically compute the corresponding diffusivities in terms of data of the dual background black hole solution. In holographic quantum critical low temperature phases, we show that these diffusivities are governed by universal relaxation of the phonons into the heat current when the dynamical critical exponent z > 2. Finally, we compute the spectrum of transverse collective modes and show that their dispersion relation matches the dispersion relation of the shear sound modes of the hydrodynamic theory of crystalline solidseng© The Authors 2019. 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 creditedhttps://creativecommons.org/licenses/by/4.0/Holography and condensed matter physics (AdS/CMT)Global symmetriesSpace-Time symmetriesjournal article10.1007/JHEP10(2019)0681029-8479open access