2020/11/30 by Daniel Arean, Daniel Areán, Richard A. Davison +2
Physics and Astronomy · #Black Holes and Theoretical Physics #Critical exponent #Critical frequency #Critical phenomena #Critical point (mathematics) #Field (mathematics) #Function (biology) #Noncommutative and Quantum Gravity Theories #Operator (biology) #Quantum #Quantum dynamics #Scaling #Topological Materials and Phenomena #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevx.11.031024
published as Phys. Rev. X 11, 031024 (2021) · v3: Matches published version; v2: Minor edits, references and one figure added; v1: 16+34 pages, 10 figures
openalex created_date 2020/12/07 · openalex publication_date 2021/07/29 · arxiv created 2021/08/10 · arxiv updated 2021/08/11 · openalex updated_date 2026/08/05
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.