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arXiv 2011.12301hep-thcond-mat.str-el
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AdS $_2$量子临界点附近的流体动力学扩散及其破裂

Hydrodynamic diffusion and its breakdown near AdS$_2$ quantum critical points

Daniel Arean, Richard A. Davison, Blaise Goutéraux, Kenta Suzuki

备注：
v3: Matches published version; v2: Minor edits, references and one figure added; v1: 16+34 pages, 10 figures
发表信息：
Phys. Rev. X 11, 031024 (2021)
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摘要：

流体力学提供了一个在足够长的时间和波长的相互作用量子场论的通用描述，但在尺度上依赖于理论的微观细节。在量子临界点附近，动力学的某些方面是普遍的，并由临界点的性质决定。我们使用规范-引力对偶性来研究两个低温状态下的扩散流体动力学的破裂，这两个低温状态是与AdS $_2$视界的黑洞对偶的，它们表现出量子临界动力学，具有时间上的涌现标度对称性。我们发现，击穿的特点是由延迟格林函数的扩散极点与一个极点与AdS $_2$区域的几何形状，使局部平衡时间设置的红外性质的理论之间的碰撞。碰撞时的频率和波矢的绝对值（$ω_{eq}$和$k_{eq}$）通过$D=ω_{eq}/k_{eq}^2$提供了状态的所有低温扩散率$D$的自然表征，其中$ω_{eq}=2πΔT$由温度$T$和红外量子临界理论的算子的标度维数$Δ$设置。我们证实，这些关系也满足在SYK链模型的强相互作用的限制。我们的工作为更深入地理解量子临界阶段的传输铺平了道路。

英文摘要：

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 ($ω_{eq}$ 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 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.

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