TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.1.010
TI  - Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
PY  - 2025/01/10
UR  - https://www.scipost.org/SciPostPhys.18.1.010
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 1
SP  - 010
A1  - Safonova, Elizaveta
AU  - Feigel'man, Mikhail V.
AU  - Kravtsov, Vladimir
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.18.1.010,
	title={{Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach}},
	author={Elizaveta Safonova and Mikhail Feigel'man and Vladimir Kravtsov},
	journal={SciPost Phys.},
	volume={18},
	pages={010},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.1.010},
	url={https://scipost.org/10.21468/SciPostPhys.18.1.010},
}