Random matrix model for eigenvalue statistics in random spin systems

We propose a working strategy to describe the eigenvalue statistics of random spin systems along whole phase diagram with thermal many-body localization (MBL) transition. Our relies on two matrix (RM) models well-defined construction, namely mixed (Brownian) ensemble and Gaussian β ensemble. show both RM are capable capturing lowest-order level correlations during transition, while deviations become non-negligible when fitting higher-order ones. Specifically, will underestimate longer-range correlations, opposite is true for Strikingly, simple average these gives nearly perfect description at all disorder strengths, even around critical region, which indicates interaction range strength between levels dominant features that responsible