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Highfrequency transport and zerosound 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:  20220817 
Date submitted:  20220812 10:45 
Submitted by:  Aleksey, Lunkin 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

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 interdot tunneling are considered in the nonFermiliquid temperature range $T \gg T_{FL}$. We take into account softmode 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 particlehole asymmetry parameter $\mathcal{E}$. At lowfrequencies $\omega \ll T$ we find the Lorenz ratio $L = \kappa(0,0)/T\sigma(0,0)$ to be nonuniversal and temperaturedependent. 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 "zerosound", known for Fermiliquids. We demonstrate also that the developed approach makes it possible to understand the origin of heavy Fermi liquids with anomalously large KadowakiWoods 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 pointbypoint 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 JakiwTeitelboim 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 (1112) 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 crosscheck" 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)