Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
Abstrak
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.
Topik & Kata Kunci
Penulis (1)
Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov
Akses Cepat
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Cek di sumber asli →- Tahun Terbit
- 2025
- Sumber Database
- DOAJ
- DOI
- 10.21468/SciPostPhys.18.1.010
- Akses
- Open Access ✓