Long-range spectral statistics of the Rosenzweig-Porter model

Wouter Buijsman

Published 2023-09-25Version 1

The Rosenzweig-Porter model is a single-parameter random matrix ensemble that supports an ergodic, fractal, and localized phase. The names of these phases refer to the properties of the (bulk) eigenstates. This work focuses on the long-range spectral statistics of the recently introduced unitary equivalent of this model. By numerically studying the Thouless time obtained from the spectral form factor, it is argued that long-range spectral statistics can be used to probe the transition between the ergodic and the fractal phases. Provided that the transition between the fractal and the localized phases can be probed through short-range level statistics such as the average ratio of consecutive level spacings, this work establishes that spectral statistics are sufficient to probe both transitions present in the phase diagram.