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Circular Rosenzweig-Porter random matrix ensemble

by Wouter Buijsman and Yevgeny Bar Lev

This Submission thread is now published as

Submission summary

As Contributors: Yevgeny Bar Lev · Wouter Buijsman
Preprint link: scipost_202111_00039v2
Date accepted: 2022-02-14
Date submitted: 2021-12-23 07:41
Submitted by: Buijsman, Wouter
Submitted to: SciPost Physics
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.

Published as SciPost Phys. 12, 082 (2022)



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.


Reports on this Submission

Anonymous Report 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.

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Report 2 by Vladimir Kravtsov 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 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: -
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