Hydrodynamic diffusion and its breakdown near AdS$_2$ quantum critical points

TL;DR

This paper investigates the breakdown of hydrodynamic diffusion near AdS$_2$ quantum critical points using gauge-gravity duality, revealing universal relations between diffusion constants, critical scaling, and IR properties, confirmed in SYK models.

Contribution

It introduces a universal characterization of diffusive breakdown near AdS$_2$ quantum critical points and connects IR properties to diffusion constants, validated by SYK chain models.

Findings

Breakdown of hydrodynamics characterized by pole collision in Green's functions.

Diffusivity relates to IR scaling and temperature via $D=\omega_{eq}/k_{eq}^2$.

Confirmed relations hold in SYK chain models at strong coupling.

Abstract

Hydrodynamics provides a universal description of interacting quantum field theories at sufficiently long times and wavelengths, but breaks down at scales dependent on microscopic details of the theory. In the vicinity of a quantum critical point, it is expected that some aspects of the dynamics are universal and dictated by properties of the critical point. We use gauge-gravity duality to investigate the breakdown of diffusive hydrodynamics in two low temperature states dual to black holes with AdS$_2$ horizons, which exhibit quantum critical dynamics with an emergent scaling symmetry in time. We find that the breakdown is characterized by a collision between the diffusive pole of the retarded Green's function with a pole associated to the AdS$_2$ region of the geometry, such that the local equilibration time is set by infra-red properties of the theory. The absolute values of the frequency and wavevector at the collision ($\omega_{eq}$ and $k_{eq}$) provide a natural characterization of all the low temperature diffusivities $D$ of the states via $D=\omega_{eq}/k_{eq}^2$ where $\omega_{eq}=2\pi\Delta T$ is set by the temperature $T$ and the scaling dimension $\Delta$ of an operator of the infra-red quantum critical theory. We confirm that these relations are also satisfied in an SYK chain model in the limit of strong interactions. Our work paves the way towards a deeper understanding of transport in quantum critical phases.