Gapless and gapped holographic phonons

TL;DR

This paper investigates a holographic model with both spontaneous and explicit translation symmetry breaking, analyzing the resulting (pseudo)-phonons, their damping, pinning, and universal relations in a condensed matter context.

Contribution

It introduces a holographic framework combining spontaneous and explicit breaking mechanisms, extending understanding of phonon dynamics and universal damping relations.

Findings

Gapless phonons with momentum relaxation when no condensate source is present.

Phonons become damped and pinned with a condensate source.

Universal relation between phonon damping, mass, and diffusivity holds for weak explicit breaking.

Abstract

We study a holographic model where translations are both spontaneously and explicitly broken, leading to the presence of (pseudo)-phonons in the spectrum. The weak explicit breaking is due to two independent mechanisms: a small source for the condensate itself and additional linearly space-dependent marginal operators. The low energy dynamics of the model is described by Wigner crystal hydrodynamics. In absence of a source for the condensate, the phonons remain gapless, but momentum is relaxed. Turning on a source for the condensate damps and pins the phonons. Finally, we verify that the universal relation between the phonon damping rate, mass and diffusivity reported in arXiv:1812.08118 continues to hold in this model for weak enough explicit breaking.