Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach

Abstract

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.

16 pages, 10 figures

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Cited by in corpus (4)

• Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles
• Local Density of States Correlations in the Lévy-Rosenzweig-Porter random matrix ensemble
• Anderson localisation in spatially structured random graphs
• Density of states correlations in Lévy Rosenzweig-Porter model via supersymmetry approach