Lévy-Rosenzweig-Porter random matrix ensemble

In this paper, we consider an extension of the Rosenzweig-Porter model, L\'evy-RP (L-RP) in which off-diagonal matrix elements are broadly distributed, providing a more realistic benchmark to develop effective description nonergodic extended (NEE) states interacting many-body disordered systems. We put forward simple, general, and intuitive argument that allows one unveil multifractal structure minibands local spectrum when hybridization is due anomalously large transition amplitudes tails distribution. The idea energy spreading can be determined self-consistently by requiring maximal rate ${\mathcal{H}}_{ij}$ between site $i$ other ${N}^{{D}_{1}}$ sites support set same order Thouless itself ${N}^{{D}_{1}\ensuremath{-}1}$. This yields fractal dimensions characterize statistics wave functions NEE phase, as well whole phase diagram L-RP ensemble. Its predictions confirmed both analytically, thorough investigation self-consistent equation for density obtained using cavity approach, numerically, via extensive exact diagonalizations.