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

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.

arXiv commentv3: Matches published version; v2: Minor edits, references and one figure added; v1: 16+34 pages, 10 figures

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