Thermal diffusivity and chaos in metals without quasiparticles

Abstract

We study the thermal diffusivity $D_T$ in models of metals without quasiparticle excitations (`strange metals'). The many-body quantum chaos and transport properties of such metals can be efficiently described by a holographic representation in a gravitational theory in an emergent curved spacetime with an additional spatial dimension. We find that at generic infra-red fixed points $D_T$ is always related to parameters characterizing many-body quantum chaos: the butterfly velocity $v_B$, and Lyapunov time $\tau_L$ through $D_T \sim v_B^2 \tau_L$. The relationship holds independently of the charge density, periodic potential strength or magnetic field at the fixed point. The generality of this result follows from the observation that the thermal conductivity of strange metals depends only on the metric near the horizon of a black hole in the emergent spacetime, and is otherwise insensitive to the profile of any matter fields.