Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Higher derivative corrections to incoherent metallic transport in holography

Matteo Baggioli, Blaise Goutéraux, Elias Kiritsis, Wei-Jia Li

TL;DR

This work investigates how higher-derivative couplings between charge and translation-symmetry breaking sectors in holographic models affect diffusion bounds in the incoherent transport regime. Using two main models (a $\mathcal{J}$-type coupling and a $\mathcal{W}(X,Y)$-type coupling with variants), the authors compute DC thermoelectric conductivities and diffusion constants, showing that while energy diffusion remains governed by the bound $D_e/v_B^2 \gtrsim \hbar/(k_B T)$, the charge diffusion bound can be driven arbitrarily close to zero by the higher-derivative terms, subject to stability constraints. They demonstrate these effects across several constructions, including arbitrary $V(X)$ potentials, and verify a Kelvin-like relation for the zero-temperature limit. The results imply that the proposed charge-diffusion bound is not universal at finite density and can be substantially violated, while the energy-diffusion bound is more robust, thereby refining the link between diffusion, chaos, and Planckian timescales in strongly coupled systems.

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.

Higher derivative corrections to incoherent metallic transport in holography

TL;DR

This work investigates how higher-derivative couplings between charge and translation-symmetry breaking sectors in holographic models affect diffusion bounds in the incoherent transport regime. Using two main models (a -type coupling and a -type coupling with variants), the authors compute DC thermoelectric conductivities and diffusion constants, showing that while energy diffusion remains governed by the bound , the charge diffusion bound can be driven arbitrarily close to zero by the higher-derivative terms, subject to stability constraints. They demonstrate these effects across several constructions, including arbitrary potentials, and verify a Kelvin-like relation for the zero-temperature limit. The results imply that the proposed charge-diffusion bound is not universal at finite density and can be substantially violated, while the energy-diffusion bound is more robust, thereby refining the link between diffusion, chaos, and Planckian timescales in strongly coupled systems.

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 , the saturation of which provides a mechanism for the T-linear resistivity of bad metals. This bound features a characteristic velocity , which was later argued to be the butterfly velocity , 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 , by potentially making the coefficient of its right-hand side arbitrarily small. On the other hand, the bound on energy diffusion is not affected.

Paper Structure

This paper contains 34 sections, 132 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The holographic models
  3. Model 1: the $\mathcal{J}$ coupling
  4. Model 2: $\mathcal{W}(X,F^2/4)$ action
  5. Stability
  6. DC thermoelectric conductivities
  7. Model 1
  8. Model 2
  9. About the Kelvin formula
  10. Impact of higher derivative couplings on the diffusivity bounds
  11. Model 1: the $\mathcal{J}$ coupling
  12. Model $2_U$
  13. Model $2_\mathcal{K}$: the $\mathcal{K}$ coupling
  14. Arbitrary Stückelberg potential $V(X)$
  15. Discussion
  16. ...and 19 more sections

Figures (2)

  • Figure 1: Physical quantities in the incoherent limit for the specific model $2_\mathcal{K}$: $U(X)=1+\mathcal{K}X$. Left: Susceptibility in units of k as a function of ${\mathcal{K}}$. The dashed red line has been added manually because Mathematica was not able to plot the function in its whole domain. Right : Incoherent conductivity as a function of ${\mathcal{K}}$.
  • Figure 2: Incoherent limit of $\frac{D_c\,T}{v_B^2}$ in function of the $\mathcal{K}$ parameter for the choice $U(X)=1+\mathcal{K}X$. The dashed line is the bound in the case $\mathcal{K}=0$.