# Universal relaxation in a holographic metallic density wave phase

## TL;DR

This paper reveals a universal relaxation mechanism for pinned density waves in holographic models, linking collective mode damping to material properties and explaining transport phenomena in high-temperature superconductors.

## Contribution

It introduces a universal formula for the damping rate of collective modes in density wave phases using gauge/gravity duality and effective field theory.

## Key findings

- The damping rate is proportional to the shear modulus and the square of the pinning mass.
- Resistivity becomes linear in temperature at low temperatures.
- Spectral weight shifts from a pinning peak to a Drude-like peak in conductivity.

## Abstract

In this work, we uncover a universal relaxation mechanism of pinned density waves, combining Gauge/Gravity duality and effective field theory techniques. Upon breaking translations spontaneously, new gapless collective modes emerge, the Nambu-Goldstone bosons of broken translations. When translations are also weakly broken (eg by disorder or lattice effects), these phonons are pinned with a mass $m$ and damped at a rate $\Omega$, which we explicitly compute. This contribution to $\Omega$ is distinct from that of topological defects. We show that $\Omega\simeq G m^2\Xi$, where $G$ is the shear modulus and $\Xi$ is related to a diffusivity of the purely spontaneous state. This result follows from the smallness of the bulk and shear moduli, as would be the case in a phase with fluctuating translational order. At low temperatures, the collective modes relax quickly into the heat current, so that late time transport is dominated by the thermal diffusivity. In this regime, the resistivity in our model is linear in temperature and the ac conductivity displays a significant rearranging of the degrees of freedom, as spectral weight is shifted from an off-axis, pinning peak to a Drude-like peak. These results could shed light on transport properties in cuprate high $T_c$ superconductors, where quantum critical behavior and translational order occur over large parts of the phase diagram and transport shows qualitatively similar features.