  In 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 solids.
