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High-frequency transport and zero-sound in an array of SYK quantum dots
by Aleksey. V. Lunkin, Mikhail . V. Feigel'man
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Submission summary
| Authors (as registered SciPost users): | Lunkin Aleksey · Mikhail Feigel'man |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2112.11500v3 (pdf) |
| Date accepted: | 2022-08-17 |
| Date submitted: | 2022-08-12 10:45 |
| Submitted by: | Aleksey, Lunkin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range $T \gg T_{FL}$. We take into account soft-mode fluctuations and demonstrate their relevance for physical observables. Electric $\sigma(\omega,p)$ and thermal $\kappa(\omega,p)$ conductivities are calculated as functions of frequency and momentum for arbitrary values of the particle-hole asymmetry parameter $\mathcal{E}$. At low-frequencies $\omega \ll T$ we find the Lorenz ratio $L = \kappa(0,0)/T\sigma(0,0)$ to be non-universal and temperature-dependent. At $\omega \gg T$ the conductivity $\sigma(\omega,p)$ contains a pole with nearly linear dispersion $\omega \approx sp\sqrt{\ln\frac{\omega}{T}}$ reminiscent of the "zero-sound", known for Fermi-liquids. We demonstrate also that the developed approach makes it possible to understand the origin of heavy Fermi liquids with anomalously large Kadowaki-Woods ratio.
Author comments upon resubmission
Dear Editors,
please find the updated version of our manuscript, with comments from the 2nd Referee taken into account. We have performed the requested small changes: the abstract and introduction were extended, and typos were corrected.
Below we would like to answer point-by-point the second referee report which includes 11 comments.
- Introduction and abstract were extended (see the end of the first page and beginning of the second page for changes in the Introduction).
- the sentence where Jakiw-Teitelboim gravitation was mentioned is now removed
- We added information about J at the beginning of the Introduction
- The sentence mentioned by the Referee was corrected
- We added a statement on the symmetric properties of the tensors
- In general, it is possible to write the mentioned sum with only one term but it leads to the additional symmetry for tunneling amplitude. We decided to write two terms but without any symmetry limitations on t.
- We removed sources from eq.(5)
- We added chemical potential to the Hamiltonian
- We added the reference to the paper where the solution (11-12) was provided originally.
- We fixed equations in accordance with the Referee's comment.
- We do not agree with Referee's statement that "absence of numerical cross-check" constitutes a weakness of our present research. All calculations described in this manuscript are parametrically exact. We did not employ any uncontrolled approximations or hypotheses. Therefore there is no reason to "support" these results by numerics.
All mentioned typos were fixed.
We believe that now our manuscript is ready for publication.
Sincerely yours,
Aleksey Lunkin and Mikhail Feigel'man
Published as SciPost Phys. 13, 073 (2022)