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Circular Rosenzweig-Porter random matrix ensemble

by Wouter Buijsman and Yevgeny Bar Lev

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Submission summary

Authors (as registered SciPost users): Yevgeny Bar Lev · Wouter Buijsman
Submission information
Preprint Link: scipost_202111_00039v2  (pdf)
Date accepted: 2022-02-14
Date submitted: 2021-12-23 07:41
Submitted by: Buijsman, Wouter
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical

Abstract

The Rosenzweig-Porter random matrix ensemble serves as a qualitative phenomenological model for the level statistics and fractality of eigenstates across the many-body localization transition in static systems. We propose a unitary (circular) analogue of this ensemble, which similarly captures the phenomenology of many-body localization in periodically driven (Floquet) systems. We define this ensemble as the outcome of a Dyson Brownian motion process. We show numerical evidence that this ensemble shares some key statistical properties with the Rosenzweig-Porter ensemble for both the eigenvalues and the eigenstates.

List of changes

Section 2
- Elaborated on the notion that we are studying level statistics on a microscopic scale.

Section 3
- Clarified on the unitarity of $S(t)$.

Section 4

- Elaborated more on the algorithm used to generate numerical data.

- Corrected a misprint on the interpretation of the finite-size scaling collapse.

Section 5
- Added Ref. [68] (resubmission).

References
- Fixed misprints mentioned in the reports.

- Updated Ref. [24] (resubmission) from the preprint to the published version.

- Updated Ref. [67] (resubmission) from the preprint to the published version.

Published as SciPost Phys. 12, 082 (2022)


Reports on this Submission

Report #3 by Anonymous (Referee 3) on 2021-12-23 (Invited Report)

Report

I believe the authors have satisfactorily allayed my previous concerns, and have improved their work following the thorough comments of the other reviewers.

  • validity: -
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Report #2 by Vladimir Kravtsov (Referee 2) on 2021-12-23 (Contributed Report)

Report

I am fully satisfied by the amendments recommended my me. The paper can by published.

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Report #1 by Ivan Khaymovich (Referee 1) on 2021-12-23 (Invited Report)

Report

In the revised version of the manuscript the authors carefully addressed all the comments of all three referees and now the manuscript is ready to be published in SciPost Physics.

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