Conductivity of a strange metal: from holography to memory functions

TL;DR

This work addresses transport in nonquasiparticle strange metals at finite density by unifying holographic methods with the memory-function formalism. Using an Einstein-Maxwell-dilaton bulk plus a small translational-symmetry-breaking scalar, the authors derive a universal Drude peak $\sigma(\omega)=\sigma_{\mathrm{dc}}/(1- i\omega\tau)$ and show that the holographically computed $\tau$ exactly matches the memory-function definition derived from low-frequency current-momentum correlations. They provide explicit horizon-data expressions linking $\tau$ to microscopic translation-breaking details and demonstrate equal results for the Seebeck coefficient $\alpha(\omega)$. The main result is an exact holography-memory-function correspondence in this regime, with potential extensions to strong momentum dissipation and more exotic translation-breaking mechanisms. This solidifies a physical picture where holographic strange metals behave hydrodynamically with universal transport features encoded by horizon data.

Abstract

We study the electrical response of a wide class of strange metal phases without quasiparticles at finite temperature and charge density, with explicitly broken translational symmetry, using holography. The low frequency electrical conductivity exhibits a Drude peak, so long as momentum relaxation is slow. The relaxation time and the direct current conductivity are exactly equal to what is computed, independently of holography, via the memory function framework.