Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $\rho(E)$ 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 tran...
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2025-01-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.1.010 |
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| author | Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov |
| author_facet | Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov |
| author_sort | Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov |
| collection | DOAJ |
| description | By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $\rho(E)$ 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 $\rho(E)$ 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. |
| format | Article |
| id | doaj-art-001d7cf3198748e6961656ab6297c935 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-001d7cf3198748e6961656ab6297c9352025-01-10T12:59:16ZengSciPostSciPost Physics2542-46532025-01-0118101010.21468/SciPostPhys.18.1.010Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approachElizaveta Safonova, Mikhail Feigel'man, Vladimir KravtsovBy using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $\rho(E)$ 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 $\rho(E)$ 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.https://scipost.org/SciPostPhys.18.1.010 |
| spellingShingle | Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach SciPost Physics |
| title | Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach |
| title_full | Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach |
| title_fullStr | Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach |
| title_full_unstemmed | Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach |
| title_short | Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach |
| title_sort | spectral properties of levy rosenzweig porter model via supersymmetric approach |
| url | https://scipost.org/SciPostPhys.18.1.010 |
| work_keys_str_mv | AT elizavetasafonovamikhailfeigelmanvladimirkravtsov spectralpropertiesoflevyrosenzweigportermodelviasupersymmetricapproach |