Long-range spectral statistics of the Rosenzweig-Porter model

Understand

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 (midspectrum) 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.