Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach

Abstract

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 $\omega \le \Gamma$\, (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 obtainen 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.

arXiv comment25 pages, 3 pictures

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