From ergodic to non-ergodic chaos in Rosenzweig-Porter model

Understand

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.