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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
| Authors (as registered SciPost users): | Yevgeny Bar Lev · Wouter Buijsman |
| Submission information | |
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| 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 | |
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| Academic field: | Physics |
| Specialties: |
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| 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 #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.
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.