# Thermal diffusivity and chaos in metals without quasiparticles

## TL;DR

This paper demonstrates a universal relationship between thermal diffusivity and quantum chaos parameters in strange metals without quasiparticles, using holographic models to connect transport properties with black hole horizon metrics.

## Contribution

It establishes a universal link between thermal diffusivity and chaos parameters in strange metals via holographic duality, independent of charge density or external fields.

## Key findings

- Thermal diffusivity relates to butterfly velocity and Lyapunov time as D_T ~ v_B^2 τ_L.
- The relationship holds at generic IR fixed points regardless of external conditions.
- Thermal conductivity depends only on the near-horizon metric of the black hole in the holographic model.

## 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.