Higher derivative corrections to incoherent metallic transport in holography

TL;DR

This paper investigates how higher derivative corrections in holographic models influence the proposed lower bounds on charge and energy diffusion in incoherent metallic transport, revealing that charge diffusion bounds can be significantly altered.

Contribution

It introduces higher derivative corrections to holographic models of disordered metals and demonstrates their strong impact on the charge diffusion bound, while leaving the energy diffusion bound unchanged.

Findings

Higher derivative terms can make the charge diffusion bound coefficient arbitrarily small.

The energy diffusion bound remains unaffected by these corrections.

The results connect holographic models, quantum chaos, and transport bounds in disordered metals.

Abstract

Transport in strongly-disordered, metallic systems is governed by diffusive processes. Based on quantum mechanics, it has been conjectured that these diffusivities obey a lower bound $D/v^2\gtrsim \hbar/k_B T$, the saturation of which provides a mechanism for the T-linear resistivity of bad metals. This bound features a characteristic velocity $v$, which was later argued to be the butterfly velocity $v_B$, based on holographic models of transport. This establishes a link between incoherent metallic transport, quantum chaos and Planckian timescales. Here we study higher derivative corrections to an effective holographic action of homogeneous disorder. The higher derivative terms involve only the charge and translation symmetry breaking sector. We show that they have a strong impact on the bound on charge diffusion $D_c/v_B^2\gtrsim \hbar/k_B T$, by potentially making the coefficient of its right-hand side arbitrarily small. On the other hand, the bound on energy diffusion is not affected.