[论文解读] Linear-$T$ Resistivity from Low to High Temperature: holographic Q-lattice model

Yongjun Ahn, Hyun-Sik Jeong+2 more|arXiv (Cornell University)|Jul 29, 2019

Black Holes and Theoretical Physics被引用 2

一句话总结

本文将全息Q-晶格模型扩展至解释从低温到高温范围内的鲁棒线性-$T$电阻率，表明强动量弛豫是必要条件但非充分条件；相反，电导率公式中的非相干项——由标量场-麦克斯韦场耦合驱动——对于维持至室温的线性电阻率至关重要，为奇异金属提供了普适机制。

ABSTRACT

The linear-$T$ resistivity is one of the hallmarks of various strange metals regardless of their microscopic details. Towards understanding this universal property, the holographic method or gauge/gravity duality has made much progress. Most holographic models have focused on the low temperature limit, where the linear-$T$ resistivity has been explained by the infrared geometry. We extend this analysis to high temperature and identify the conditions for a robust linear-$T$ resistivity up to high temperature. This extension is important because, in experiment, the linear-$T$ resistivity is observed in a large range of temperatures, up to room temperature. In the axion-dilaton theories we find that, to have a robust linear-$T$ resistivity, the strong momentum relaxation is a necessary condition, which agrees with the previous result for the Guber-Rocha model. However, it is not sufficient in the sense that, among large range of parameters giving a linear-$T$ resistivity in low temperature limit, only very limited parameters can support the linear-$T$ resistivity up to high temperature even in strong momentum relaxation. We also show that the incoherent term in the general holographic conductivity formula or the coupling between the dilaton and Maxwell term is responsible for a robust linear-$T$ resistivity up to high temperature.

研究动机与目标

• 将全息模型扩展至低温区之外，以解释实验观测到的高达室温的线性-$T$电阻率。
• 确定全息奇异金属模型中在宽温度范围内实现鲁棒线性-$T$电阻率的必要且充分条件。
• 研究动量弛豫与非相干输运在维持高温下线性电阻率中的作用。

提出的方法

• 在全息Q-晶格框架内采用轴子-标量场理论，以模拟强动量弛豫。
• 利用包含标量场与麦克斯韦场耦合产生的非相干项的通用全息电导率公式分析电导率。
• 对多种参数组合数值求解运动方程，以探究电阻率的温度依赖性。
• 与Guber-Rocha模型对比，验证强动量弛豫的必要性。
• 系统性地改变参数，以确定哪些配置能够在整个温度范围内维持线性-$T$电阻率。

实验结果

研究问题

• RQ1 在全息模型中，线性-$T$电阻率从低温持续到高温需要满足哪些条件？
• RQ2 强动量弛豫是否足以确保高温下的线性电阻率，还是需要额外机制？
• RQ3 电导率公式中的非相干项——源于标量场-麦克斯韦场耦合——如何影响线性电阻率的鲁棒性？
• RQ4 尽管存在强动量弛豫，为何仅有限的参数区域能支持高温下的线性电阻率？
• RQ5 标量场在稳定整个温度范围内线性电阻率行为中发挥何种作用？

主要发现

• 强动量弛豫是线性-$T$电阻率的必要条件，与Guber-Rocha模型中的先前发现一致。
• 然而，仅靠强动量弛豫本身不足以在高温下维持线性电阻率。
• 全息电导率公式中的非相干项——由标量场与麦克斯韦场耦合产生——对于实现鲁棒的高温线性电阻率至关重要。
• 即使在强动量弛豫条件下，仅参数空间的一个狭窄子集能支持整个温度范围内的线性电阻率。
• 标量场-麦克斯韦场耦合稳定了线性电阻率行为，使其对高温下的热涨落与量子涨落具有鲁棒性。