A holographic strange metal with slowly fluctuating translational order

We study the interplay between weakly-pinned translational order and quantum criticality in a strongly-coupled metallic phase using Gauge/Gravity duality. Translations are spontaneously broken by the condensation of neutral scalar fields in the bulk, and generate new gapless degrees of freedom (the phonons) in the dual field theory. When translations are explicitly broken, the phonons are both pinned with a mass $m$ and damped at a rate $\Omega$. Two distinct effective theories of charge dynamics apply: at high temperatures, the pseudo-phonons dominate and the ac conductivity displays a finite frequency peak corresponding to the pinned collective mode; at low temperatures, the pseudo-phonons are sub-dominant, the system behaves like a fluid with slow momentum relaxation and the ac conductivity is Drude-like. Drude-like peaks moving off axis with increasing temperature are also observed in bad metals and cuprate strange metals, where translational order and quantum criticality are both believed to play a central role. In the phonon-dominated regime, the phonon damping rate is simply related to their mass through a diffusivity of the spontaneous system, $\Omega\simeq m^2\xi$. We expect this relation to hold more generally in systems with fluctuating translational order. At low temperatures, the system saturates an entropy bound, whose origin is universal relaxation of the phonons into the heat current.