Effective holographic theory of charge density waves

TL;DR

This paper develops a holographic model for charge density waves using Gauge/Gravity duality, capturing phonon dynamics and translation symmetry breaking, and analyzes conductivity properties at quantum critical points.

Contribution

It introduces a simple gravity model with spontaneous translation symmetry breaking and explores its stability and conductivity behavior at quantum critical points.

Findings

Including quartic derivative terms causes instabilities and stable translation-breaking phases.

Analytical computation of the real part of electric conductivity.

Construction of Lifshitz-like hyperscaling violating ground states with variable conductivity.

Abstract

We use Gauge/Gravity duality to write down an effective low energy holographic theory of charge density waves. We consider a simple gravity model which breaks translations spontaneously in the dual field theory in a homogeneous manner, capturing the low energy dynamics of phonons coupled to conserved currents. We first focus on the leading two-derivative action, which leads to excited states with non-zero strain. We show that including subleading quartic derivative terms leads to dynamical instabilities of AdS$_2$ translation invariant states and to stable phases breaking translations spontaneously. We compute analytically the real part of the electric conductivity. The model allows to construct Lifshitz-like hyperscaling violating quantum critical ground states breaking translations spontaneously. At these critical points, the real part of the dc conductivity can be metallic or insulating.