Thermal diffusivity and chaos in metals without quasiparticles

TL;DR

The paper investigates thermal transport in strange metals without quasiparticles through holographic Q-lattice models, focusing on the relationship between thermal diffusivity $D_T$ and quantum-chaos parameters via horizon data. It demonstrates that near generic IR fixed points with Lifshitz or hyperscaling-violating geometries, $D_T = \frac{z}{2 z - 2} v_B^2 \tau_L$, with $\tau_L = (2 \pi T)^{-1}$ and $v_B$ set by the near-horizon metric, independent of UV details such as density, lattice strength, or magnetic field. The key technical advance is showing that the dc thermal conductivity $\kappa$ can be expressed purely in terms of the near-horizon geometry, enabling a universal chaos-diffusivity relation that persists under magnetic fields and extends to anisotropic and DBI scenarios; special cases like $z=1$ and AdS$_2 \times \mathbb{R}^d$ are discussed with modified coefficients. This establishes a robust, horizon-driven link between chaos and diffusion in incoherent metals, with potential experimental relevance for thermal diffusion in strongly correlated systems.

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 $τ_L$ through $D_T \sim v_B^2 τ_L$. 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.