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.
Highlights
Interacting quantum field theories are notoriously challenging, especially when there is no quasiparticlebased description of the state
At long times and wavelengths, hydrodynamics provides an effective description of a system in terms of a few conserved quantities dictated by symmetries [13,14,15]
We study the breakdown of hydrodynamics in certain low-temperature (T) states dual to black holes with nearly extremal AdS2 × R2 near-horizon metrics
Summary
Interacting quantum field theories are notoriously challenging, especially when there is no quasiparticlebased description of the state. Our first result is that the breakdown is caused by modes associated to the AdS2 region of the geometry, and as a consequence ωeq is set by universal (i.e., infrared) data via ωeq → 2πΔT as T → 0; ð1Þ where Δ is the infrared scaling dimension of the least irrelevant operator that couples to the diffusion mode This is in contrast to systems with a weakly broken symmetry, for which ωeq ≪ T, but is in line with the expectation that the quantum critical dynamics is controlled by a “Planckian” timescale τeq ∼ 1=T [29,63]. Technical details of our calculations are presented in Supplemental Material [76]
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