Loop current fluctuations and quantum critical transport
Loop current fluctuations and quantum critical transport
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DOI：
10.21468/scipostphys.14.5.113
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发表时间：
2022-08
期刊：
影响因子：
5.5
通讯作者：
Zheng Shi;D. Else;Hart Goldman;T. Senthil
中科院分区：
文献类型：
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作者：
Zheng Shi;D. Else;Hart Goldman;T. Senthil
我们研究电输运在量子临界点（QCPs）与回路电流在金属中的排序，特别是专注于模型的“赫兹-米利斯”型。在红外（IR）固定点和在没有无序的情况下，最简单的这样的模型具有无限的DC电导率和零非相干电导率在非零频率。然而，我们发现一个特殊的变形，涉及在味空间中具有随机耦合的NN种玻色子和费米子，在IR固定点处允许有限的非相干的、依赖于频率的电导率，\sigma（\omega>0）\sim\omega^{-2/z}σ（ω>0）<$ω−2/z，其中zz是玻色子动力学指数。利用量子反常的非微扰结构，我们发展了一种强有力的计算输运的方法。由此产生的“异常辅助大NN扩展”使我们能够系统地提取电导率。虽然我们的结果意味着这样的随机味模型作为物理N = 1 N =1系统的描述是有问题的，但它们有助于说明量子临界输运的一些一般条件以及反常辅助计算方法。此外，我们重新回顾了一个旧的结果，即在这类问题中，无关算子产生依赖于频率的电导率，\sigma（\omega>0）\sim \omega^{-2（z-2）/z}σ（ω>0）<$ω−2（z−2）/z。我们明确地表明，在原来的计算范围内，这个结果不适用于任何序参量。
We study electrical transport at quantum critical points (QCPs) associated with loop current ordering in a metal, focusing specifically on models of the “Hertz-Millis” type. At the infrared (IR) fixed point and in the absence of disorder, the simplest such models have infinite DC conductivity and zero incoherent conductivity at nonzero frequencies. However, we find that a particular deformation, involving NN species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, \sigma(\omega>0)\sim\omega^{-2/z}σ(ω>0)∼ω−2/z, where zz is the boson dynamical exponent. Leveraging the non-perturbative structure of quantum anomalies, we develop a powerful calculational method for transport. The resulting "anomaly-assisted large NN expansion" allows us to extract the conductivity systematically. Although our results imply that such random-flavor models are problematic as a description of the physical N = 1N=1 system, they serve to illustrate some general conditions for quantum critical transport as well as the anomaly-assisted calculational methods. In addition, we revisit an old result that irrelevant operators generate a frequency-dependent conductivity, \sigma(\omega>0) \sim \omega^{-2(z-2)/z}σ(ω>0)∼ω−2(z−2)/z, in problems of this kind. We show explicitly, within the scope of the original calculation, that this result does not hold for any order parameter.