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 infrared properties of the theory. The absolute values of the frequency and wave vector at the collision (ω_{eq} and k_{eq}) provide a natural characterization of all the low-temperature diffusivities D of the states via D=ω_{eq}/k_{eq}^{2}, where ω_{eq}=2πΔT is set by the temperature T and the scaling dimension Δ of an operator of the infrared quantum critical theory. We confirm that these relations are also satisfied in a Sachdev-Ye-Kitaev chain model in the limit of strong interactions. Our work paves the way toward a deeper understanding of transport in quantum critical phases.