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Spectral statistics of a minimal quantum glass model

by Richard Barney, Michael Winer, Christopher L. Baldwin, Brian Swingle, Victor Galitski

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Richard Barney
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-07-14
Date submitted: 2023-06-28 18:59
Submitted by: Barney, Richard
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approaches: Theoretical, Computational


Glasses have the interesting feature of being neither integrable nor fully chaotic. They thermalize quickly within a subspace but thermalize much more slowly across the full space due to high free energy barriers which partition the configuration space into sectors. Past works have examined the Rosenzweig-Porter (RP) model as a minimal quantum model which transitions from localized to chaotic behavior. In this work we generalize the RP model in such a way that it becomes a minimal model which transitions from glassy to chaotic behavior, which we term the "Block Rosenzweig-Porter" (BRP) model. We calculate the spectral form factors of both models at all timescales. Whereas the RP model exhibits a crossover from localized to ergodic behavior at the Thouless timescale, the new BRP model instead crosses over from glassy to fully chaotic behavior, as seen by a change in the slope of the ramp of the spectral form factor.

Author comments upon resubmission

We are grateful to the referees for their comments on our manuscript. At one referee's request we have included some discussion regarding the good agreement between the theory and numerics for the spectral form factor of the Rosenzweig-Porter model at times larger than the Heisenberg time. There is some broad discussion of differences between the Block Rosenzweig-Porter model and more physical models at the end of the final section. With the changes made we believe the manuscript is ready for publication.

List of changes

1) Concerning the SFF of the RP model, this sentence has been added at the end of the first paragraph on page 16: "Although it was derived considering only times not larger than the Heisenberg time, it continues to hold for later times, as we will discuss in the following section."
2) At the end of the second paragraph on page 16, which is a discussion of Fig. 4, we have added "For small values of $\Lambda$ we see that the SFF reaches its plateau at times greater (but not much greater) than the Heisenberg time. The agreement between theory and numerics is still very good at these late times."
3) The second-to-last paragraph of Section 4, including Eq. (82), has been added to show that the plateau behavior is recovered when time is taken to be larger than the Heisenberg time in our result for the RP SFF.
4) Additional minor edits.

Published as SciPost Phys. 15, 084 (2023)

Reports on this Submission

Anonymous Report 1 on 2023-6-29 (Invited Report)


The Authors have adressed my remarks thoroughly by adding a detailed discussion to the manuscript.

I recommend publication of the paper in its current form.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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