Colloquium: Hydrodynamics and holography of charge density wave phases

The Colloquium reviews recent progress in the effective description of strongly correlated phases of matter with spontaneously broken translations, such as charge density waves or Wigner crystals. In real materials, disorder is inevitable and pins the Goldstones of broken translations. The Colloquium describes how pinning can be incorporated into the effective field theory at low energies without making any assumptions on the presence of boost symmetry. The essential role played by gauge-gravity duality models in establishing these effective field theories with only approximate symmetries is reviewed. The Colloquium closes with a discussion on the relevance of these models to the phenomenology of dc and ac transport in strongly correlated strange and bad metals, such as high-temperature superconductors.

Figure 1

The typical curve describing the onset of the instability toward a holographic phase breaking translations spontaneously. Insets: spatial profiles of the charge density $n$ in the broken and normal phases. Adapted from [83].

Figure 2

Schematic representation of the ac conductivity (59) in the Galilean limit when $\mathrm{\Omega }$ is dialed from large (solid line) to small (bullets), keeping all other parameters fixed. The transfer of spectral weight from the zero frequency Drude-like peak to the off-axis peak is evident.