TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.20.1.003
TI  - Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach
PY  - 2026/01/12
UR  - https://scipost.org/SciPostPhys.20.1.003
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 20
IS  - 1
SP  - 003
A1  - Safonova, Elizaveta
AU  - Lunkin, Aleksey
AU  - Feigel'man, Mikhail
AB  - We studied global density-of-states correlation function $R(\omega)$ for Lévy-Rosenzweig-Porter random matrix ensemble in the non-ergodic extended phase. Using an extension of Efetov's supersymmetry approach we calculated $R(\omega)$ exactly in all relevant ranges of $\omega$. At relatively low $\omega ≤ \Gamma$ (with $\Gamma \gg \Delta$ being the effective miniband width) we found GUE-type oscillations with period of level spacing $\Delta$, decaying exponentially at the Thouless energy scale $E_{Th} = \sqrt{\Delta \Gamma/2\pi}$. At high energies $\omega \gg E_{Th}$ our results coincide with those obtained in [A. V. Lunkin and K. Tikhonov, SciPost Phys. 19, 015 (2025)] via cavity equation approach. Inverse of the effective miniband width, $1/\Gamma$, is shown to be given by the average of the local decay times over Lévy distribution.
ER  -

@Article{10.21468/SciPostPhys.20.1.003,
	title={{Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach}},
	author={Elizaveta Safonova and Aleksey Lunkin and Mikhail Feigel'man},
	journal={SciPost Phys.},
	volume={20},
	pages={003},
	year={2026},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.20.1.003},
	url={https://scipost.org/10.21468/SciPostPhys.20.1.003},
}