# Holographic transport and density waves

## TL;DR

This paper investigates how spontaneous density waves in holographic models influence heat and charge transport, revealing discontinuities in DC conductivities and spectral weight transfer at low frequencies due to symmetry breaking and pinning effects.

## Contribution

It demonstrates the impact of incommensurate density waves on transport properties in holographic lattices, including the discontinuous behavior of DC conductivities as the pinning parameter approaches zero.

## Key findings

- DC transport coefficients are discontinuous at zero pinning
- Spectral weight shifts to frequencies related to the pinning parameter
- Weak momentum relaxation causes a shift in the Drude peak

## Abstract

We consider transport of heat and charge in holographic lattices which are phases of strongly coupled matter in which translations are broken explicitly. In these systems, we study a spontaneous density wave that breaks translations incommensurately to the lattice. The emergent gapless mode due to symmetry breaking couples to the heat current impacting transport at low frequencies. We study the effects of this coupling when the mode is freely sliding as well as after the introduction of a small deformation parameter which pins down the density wave. We prove that the DC transport coefficients are discontinuous in the limit of the pinning parameter going to zero. From the perspective of finite frequency thermoelectric conductivity, this limiting process is accompanied by the transfer of spectral weight to frequencies set by the pinning parameter. As expected, for weak momentum relaxation, this spectral weight transfer appears as a shift of the Drude peak.