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.

25 pages, 3 pictures

References in corpus (11)

• Challenges to observation of many-body localization
• Many-Body Localization in the Age of Classical Computing
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Phenomenology of the Prethermal Many-Body Localized Regime
• Sensitivity of (multi)fractal eigenstates to a perturbation of the Hamiltonian
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach
• Local Density of States Correlations in the Lévy-Rosenzweig-Porter random matrix ensemble