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Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
by Elizaveta Safonova, Mikhail Feigelman, Vladimir Kravtsov
Submission summary
| Authors (as registered SciPost users): | Mikhail Feigel'man · Vladimir Kravtsov · Elizaveta Safonova |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2408.15072v2 (pdf) |
| Date submitted: | 2024-11-10 17:09 |
| Submitted by: | Safonova, Elizaveta |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $\rho(E)$ for the L\'evy and the L\'evy -Rosenzweig-Porter random matrices which off-diagonal elements are strongly non-Gaussian with power-law tails. This makes the standard Hubbard-Stratonovich transformation inapplicable to such problems. We used, instead, the functional Hubbard-Stratonovich transformation which allowed to solve the problem analytically for large sizes of matrices. We show that $\rho(E)$ depends crucially on the control parameter that drives the system through the transition between the ergodic and the fractal phases and it can be used as an order parameter.
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Author comments upon resubmission
Dear Editor,
we resubmit thereby our manuscript "Spectral properties of L\'evy Rosenzweig-Porter model via supersymmetric approach".
Recommendations from both referee reports are taken into account.
Our detailed responses to both these referee reports are posted at thepaper submission page on 2024-10-30 (2nd report) and on 2024-10-04 (1st report).
Sincerely yours, E. Safonova, M. Feigelman and V. Kravtsov
we resubmit thereby our manuscript "Spectral properties of L\'evy Rosenzweig-Porter model via supersymmetric approach".
Recommendations from both referee reports are taken into account.
Our detailed responses to both these referee reports are posted at thepaper submission page on 2024-10-30 (2nd report) and on 2024-10-04 (1st report).
Sincerely yours, E. Safonova, M. Feigelman and V. Kravtsov
Current status:
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