  The Rosenzweig-Porter model is a one-parameter family of random matrices with
three different phases: ergodic, extended non-ergodic and localized. We
characterize numerically each of these phases and the transitions between them.
We focus on several quantities that exhibit non-analytical behaviour and show
that they obey the scaling hypothesis. Based on this, we argue that non-ergodic
chaotic and ergodic regimes are separated by a continuous phase transition,
similarly to the transition between non-ergodic chaotic and localized phases.
