线性轴子全息 Gubser-Rocha 模型无法捕捉奇异金属的所有输运反常
Inability of linear axion holographic Gubser-Rocha model to capture all the transport anomalies of strange metals
AI总结：
本文证明仅有单一动量弛豫时间的线性轴子全息 Gubser-Rocha 模型虽具 T 线性电阻率，却无法解释霍尔角等双弛豫尺度反常。
摘要：
在过去十年中，受 Planckian 弛豫概念以及铜氧化物材料中可能存在量子临界点的推动，全息技术被广泛用于解决奇异金属和高 Tc 超导体问题。在各种设置中，线性轴子 Gubser-Rocha 模型常被视为有前景的奇异金属全息模型，因为它具有著名的电阻率随 T 线性变化的性质。正如 Phil Anderson 强烈主张的，除 T 线性电阻率之外，奇异金属相还存在若干独特的额外反常，例如类似 Fermi 液体的霍尔角——即著名的双弛豫尺度问题。在这篇短札记中，我们表明，只具有单一动量弛豫时间的线性轴子全息 Gubser-Rocha 模型在这一方面失败，因此无法捕捉奇异金属的输运现象学。我们通过直接数值计算、先前已证明的标度分析以及一个流体动力学论证来证明这一论断。最后，我们以乐观的讨论作结，探讨可能的改进与推广，它们或许能带来一个完整呈现奇异金属全部特征的全息模型。
英文摘要：
In the last decade, motivated by the concept of Planckian relaxation and the possible existence of a quantum critical point in cuprate materials, holographic techniques have been extensively used to tackle the problem of strange metals and high-$T_c$ superconductors. Among the various setups, the linear axion Gubser-Rocha model has often been considered as a promising holographic model for strange metals since endowed with the famous linear in $T$ resistivity property. As fiercely advocated by Phil Anderson, beyond $T$-linear resistivity, there are several additional anomalies unique to the strange metal phase, as for example a Fermi liquid like Hall angle -- the famous problem of the two relaxation scales. In this short note, we show that the linear axion holographic Gubser-Rocha model, which presents a single momentum relaxation time, fails in this respect and therefore is not able to capture the transport phenomenology of strange metals. We prove our statement by means of a direct numerical computation, a previously demonstrated scaling analysis and also a hydrodynamic argument. Finally, we conclude with an optimistic discussion on the possible improvements and generalizations which could lead to a holographic model for strange metals in all their glory.
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