Elizaveta Safonova: Nonergodic extended states in powerlaw matrix ensembles: supersymmetry approach

We present an analytical calculation for the density of states correlation function for L´evy-Rosenzweig-Porter random matrix ensemble using supersymmetry approach. Nonergodic extended phase characterizes the intermediate phase between localized and fully-ergodic regimes. In the theory of random matrices it appeared in the study of an ensemble with a distinguished diagonal. Supersymmetry approach enables to obtain the result on all the energy scales, including level spacing. However it has never been used for non-gaussian ensembles yet. During the seminar I am going to give a short overview of previous results in this field and explain the adaptation of supersymmetry approach for power-law distributed matrix elements.