Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909456257777664 |
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| author | Safonova, Elizaveta Feigelman, Mikhail Kravtsov, Vladimir |
| author_facet | Safonova, Elizaveta Feigelman, Mikhail Kravtsov, Vladimir |
| contents | By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $ρ(E)$ for the Lévy and the Lévy -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 $ρ(E)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15072 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach Safonova, Elizaveta Feigelman, Mikhail Kravtsov, Vladimir Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics Quantum Physics By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $ρ(E)$ for the Lévy and the Lévy -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 $ρ(E)$ 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. |
| title | Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2408.15072 |