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Spectral properties of L\'evy Rosenzweig-Porter model via supersymmetric approach
by Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov
Submission summary
| Authors (as registered SciPost users): | Mikhail Feigel'man · Vladimir Kravtsov · Elizaveta Safonova |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00004v1 (pdf) |
| Date submitted: | 2024-09-05 00:57 |
| 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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing