TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.1.015
TI  - Local density of states correlations in the Lévy-Rosenzweig-Porter random matrix ensemble
PY  - 2025/07/16
UR  - https://scipost.org/SciPostPhys.19.1.015
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 1
SP  - 015
A1  - Lunkin, Aleksey V.
AU  - Tikhonov, Konstantin
AB  - We present an analytical calculation of the local density of states correlation function $ \beta(\omega) $ in the Lévy-Rosenzweig-Porter random matrix ensemble at energy scales larger than the level spacing but smaller than the bandwidth. The only relevant energy scale in this limit is the typical level width $\Gamma_0$. We show that $\beta(\omega \ll \Gamma_0) \sim W/\Gamma_0$ (here $W$ is width of the band) whereas $\beta(\omega \gg \Gamma_0) \sim (W/\Gamma_0) (\omega/\Gamma_0)^{-\mu} $ where $\mu$ is an index characterising the distribution of the matrix elements. We also provide an expression for the average return probability at long times: $\ln [R(t\gg\Gamma_0^{-1})] \sim -(\Gamma_0 t)^{\mu/2}$. Numerical results based on the pool method and exact diagonalization are also provided and are in agreement with the analytical theory.
ER  -

@Article{10.21468/SciPostPhys.19.1.015,
	title={{Local density of states correlations in the Lévy-Rosenzweig-Porter random matrix ensemble}},
	author={Aleksey Lunkin and Konstantin Tikhonov},
	journal={SciPost Phys.},
	volume={19},
	pages={015},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.1.015},
	url={https://scipost.org/10.21468/SciPostPhys.19.1.015},
}