Title: Effective holographic theory of charge density waves,
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.