Loop current fluctuations and quantum critical transport

Journal Article · Mon May 15 04:00:00 EDT 2023 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.14.5.113· OSTI ID:1973725

Shi, Zhengyan Darius ^[1]; Else, Dominic V. ^[2]; Goldman, Hart ^[1]; Senthil, Todadri ^[1]

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1. Massachusetts Institute of Technology
2. Harvard University

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 N $N$ 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} $\sigma (\omega >0)\sim {\omega }^{-2/z}$ , where z $z$ 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 N $N$ 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 = 1 $N=1$ 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} $\sigma (\omega >0)\sim {\omega }^{-2(z-2)/z}$ , 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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0008739
• OSTI ID: 1973725
• Alternate ID(s): OSTI ID: 2419840
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 5 Vol. 14; ISSN 2542-4653
• Publisher: Stichting SciPost
• Country of Publication: Netherlands
• Language: English