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Non-equilibrium Sachdev-Ye-Kitaev model with quadratic perturbation

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:  (pdf)
Date submitted: 2021-09-21 11:52
Submitted by: Aleksey, Lunkin
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


We consider a non-equilibrium generalization of the mixed SYK$_4$+SYK$_2$ model and calculate the energy dissipation rate $W(\omega)$ that results due to periodic modulation of random quadratic matrix elements with a frequency $\omega$. We find that $W(\omega)$ possesses a peak at $\omega$ close to the polaron energy splitting $\omega_R$ found recently (PRL 125, 196602), demonstrating the physical significance of this energy scale. Next, we study the effect of energy pumping with a finite amplitude at the resonance frequency $\omega_R$ and calculate, in presence of this pumping, non-equilibrium dissipation rate due to low-frequency parametric modulation. We found an unusual phenomenon similar to "dry friction" in presence of pumping.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 2 on 2021-11-8 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2106.11245v2, delivered 2021-11-08, doi: 10.21468/SciPost.Report.3815


It is a very interesting paper which further deepens the understanding of the so-called reparametrization modes in the non-equilibrium setting of the SYK model perturbed by quadratic Majorana couplings. In particular, authours are able to identify the very clear manifestation of the polaron type of physics which was previously discovered by them using the gravity dual description.

The results of the paper seems to be reasonable and well theoretically justified. So, I will definitely recommend this manuscript for the publication in SciPost after some revision.

My main concern is about the clarity of presentation. It would be nice if authors elucidate a physical meaning of their starting action (7). For instance, drawing few standard diagrams showing an external pumping force and the reparametrization mode joined into 3 and 4 point vertices would help a lot for potential readers to easily grasp the physics. The same diagrams could be later used to show different contributions to the pumping rate.

One could also perhaps add the citation to

Skvortsov et al., JETP Lett. 80, 54 (2004), "Energy absorption in time-dependent unitary random matrix ensembles: dynamic vs Anderson localization"

As to me, the present manuscript constitutes a natural extension of the same problem to the case of interacting fermions.

  • validity: high
  • significance: good
  • originality: high
  • clarity: good
  • formatting: good
  • grammar: excellent

Anonymous Report 1 on 2021-10-18 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2106.11245v2, delivered 2021-10-18, doi: 10.21468/SciPost.Report.3699


The paper studies the SYK model with a quadratic perturbation and builds upon results by the same authors in previous works. The main result is a computation of the absorption rate in a model with a periodically modulated quadratic fermion term. The authors find that even though the quadratic perturbation does not significantly change the saddle, the absorption rate is significantly different from pure SYK. The results are interesting and I recommend it for publication.

Some comments:

In eqs. (7), (8), (14) I did not understand why the quadratic term $S^{(2)}$ is included with fluctuations $S_{SYK}$, while $e^{S^{(1)}}$ is expanded out. Naively, it seems that $S^{(2)}$ should be suppressed in comparison to $S^{(1)}$ and could also be treated as a small perturbation. Then the computation could be done with the SYK propagator defined by $S_{SYK}$.
Minor: a) There are some inconsistencies in the text when referring to the “action eq. 5”.Presumably the unnumbered equation between (4) and (5) is implied. b) Integration variable in eq. 30 seems to be misprinted.

  • validity: high
  • significance: good
  • originality: high
  • clarity: good
  • formatting: good
  • grammar: reasonable

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