Pinning of longitudinal phonons in holographic spontaneous helices

TL;DR

This paper investigates how a longitudinal phonon mode in a holographic model with helical symmetry becomes pinned due to explicit symmetry breaking, affecting its dispersion and leading to a metal-insulator transition.

Contribution

It is the first holographic study demonstrating phonon pinning and analyzing its effects on dispersion, conductivity, and phase transition.

Findings

Observation of phonon pinning in holography

Dependence of phonon properties on source amplitude and temperature

Identification of a metal-insulator transition

Abstract

We consider the spontaneous breaking of translational symmetry and identify the associated Goldstone mode -- a longitudinal phonon -- in a holographic model with Bianchi VII helical symmetry. For the first time in holography, we observe the pinning of this mode after introducing a source for explicit breaking compatible with the helical symmetry of our setup. We study the dispersion relation of the resulting pseudo-Goldstone mode, uncovering how its speed and mass gap depend on the amplitude of the source and temperature. In addition, we extract the optical conductivity as a function of frequency, which reveals a metal-insulator transition as a consequence of the pinning.