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Loop current fluctuations and quantum critical transport
by Zhengyan Darius Shi, Dominic V. Else, Hart Goldman, T. Senthil
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Hart Goldman · Zhengyan Shi |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202301_00005v1 (pdf) |
| Date accepted: | 2023-03-15 |
| Date submitted: | 2023-01-04 00:39 |
| Submitted by: | Shi, Zhengyan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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 $N$ species of bosons and fermions with random couplings in flavor space, admits a finite incoherent, frequency-dependent conductivity at the IR fixed point, $\sigma(\omega>0)\sim\omega^{-2/z}$, where $z$ 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 $N$ 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 $N = 1$ 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, $\sigma(\omega>0) \sim \omega^{-2(z-2)/z}$, 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.
Author comments upon resubmission
List of changes
Here we summarize substantive revisions to the manuscript in response to the comments from referees. Please note that all equation references are to the original submitted manuscript.
(1) In response to referee 1, we have clarified the regime of validity of eq (1.5) and the subtle interplay between large N and small frequency limit in the introduction.
(2) In response to referee 2, we have rephrased the paragraph below eq (3.6) to highlight the physical meaning of eq (3.6) as deformed Ward identities and relegated the comment about regularization dependence to a footnote.
(3) In response to referee 2, we have added some comments on page 16 to emphasize that many results for the loop current order QCP carry over to the case of fermions coupled to a U(1) gauge field.
(4) In response to referee 2, we have revised Section 3.4 to sequester the reanalysis of Ref.64. We have also added a signpost signaling that this reanalysis is somewhat tangential to the main line of argument and can be skipped on a first reading.
(5) In response to referee 3, we have added a paragraph at the end of Section 3.1 about the possible effects of large-angle scattering that are not included in our mid-IR patch theory.
(6) In Appendix F, we have strengthened our results by showing that, within the RPA expansion, the $\omega^{-2(z-2)/z}$ contribution to the conductivity actually vanishes for both inversion-even and inversion-odd order parameters. This is also reflected in the abstract, the introduction, and Section 3.4.
Published as SciPost Phys. 14, 113 (2023)
Reports on this Submission
Report
I agree with the authors that there exists a qualitative difference between the N=1 model and the large N counterpart with random coupling because the mechanisms that can lead to incoherent conductivity are different. I recommend the publication of the revised manuscript.