# Diffusion and universal relaxation of holographic phonons

## TL;DR

This paper uses holographic duality to analyze phonon dynamics in phases with spontaneously broken translations, revealing universal diffusivities and shear sound modes that connect to crystalline solid behavior.

## Contribution

It provides an analytical holographic model for phonon diffusion and collective modes, highlighting universal relaxation behavior at low temperatures for phases with dynamical critical exponent z>2.

## Key findings

- Diffusivities governed by universal phonon relaxation into heat current.
- Identification of shear sound modes matching crystalline solid theory.
- Analytical computation of transport coefficients from black hole backgrounds.

## Abstract

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.