Hydrodynamic diffusion and its breakdown near AdS2 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 AdS2 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 AdS2 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 (ωeq and keq) provide a natural characterization of all the low temperature diffusivities D of the states via D=ωeq/keq2 where ωeq=2π T is set by the temperature T and the scaling dimension 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.