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

2019/04/30 by M. Pino, J. Tabanera, P. Serna · 1 citation
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1088/1751-8121/ab4b76

12 pages

arxiv created 2019/05/17 · arxiv updated 2019/12/04

Abstract

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.

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