Spectral correlations in explicitly multifractal ensembles

Investigate spectral correlations, including the level compressibility and its crossover behavior, in random matrix models that exhibit explicitly multifractal eigenstates, such as sums of several random matrices with distinct fractal dimension spectra, to assess how universality extends beyond simple fractal phases.

Background

The universality found here appears to apply to models whose intermediate phase has compact mini-bands and simple fractal spectra. Many physically relevant systems display multifractal eigenstates with nontrivial spectra of fractal dimensions.

The authors suggest probing spectral correlations in ensembles constructed to be explicitly multifractal (e.g., sums of matrices with different fractal spectra) to test whether the crossover function and compressibility retain universality in that more complex setting.