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 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 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 ( and ) provide a natural characterization of all the low-temperature diffusivities of the states via , where is set by the temperature 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.
- Received 12 February 2021
- Revised 22 April 2021
- Accepted 25 May 2021
DOI:https://doi.org/10.1103/PhysRevX.11.031024
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
The processes by which a material conducts heat over short distances and times are very sensitive to what it is made of. However, over macroscopic scales, the dominant process is usually diffusion, and it is important to understand the emergence of this process from the more microscopic dynamics. This is often difficult, as the crossover regime is sensitive to the details of the system’s constituents. We have identified a class of systems in which diffusion competes with another general, collective process for heat conduction. As a consequence, the time and distance scales at which diffusion dominates in these examples are universally related to other macroscopic properties of the state.
The cases we study are examples of quantum critical phases of matter, which emerge at low temperatures when microscopic constituents interact strongly with one another and form a collective “soup” that looks the same at all scales. In one case, the microscopic constituents are electronlike particles on a lattice, while in others they are gauge fields (similar to the gluons that mediate the strong interaction in particle physics) that we study using a mathematically equivalent theory of gravity. Despite their very different microscopic origins, we show that diffusion emerges in both types of examples at a timescale inversely proportional to temperature, with a proportionality constant set by a basic property of the critical phase.
Our work paves the way for a deeper understanding of the dynamics of strongly interacting quantum critical phases, for example, those that arise in ultracold atom experiments or in heavy-ion collisions.
