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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: | Feb. 14, 2022 |
| Date submitted: | Dec. 23, 2021, 7:41 a.m. |
| 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)