Hydrodynamic Diffusion and Its Breakdown near <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>AdS</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> Quantum Critical Points
Daniel Areán, Richard A. Davison, Blaise Goutéraux, Kenta Suzuki
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 ( eq and k eq ) provide a natural characterization of all the low-temperature diffusivities D of the states via D eq =k 2 eq , where eq 2T is set by the temperature T and the scaling dimension 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.