Cat states carrying long-range correlations in the many-body localized phase

The many-body localization (MBL) problem continues to reveal its rich physical content. Herey, the authors investigate long-range correlations in the random-field Heisenberg chain and find rare, system-spanning ``cat states'' hidden in the high-energy many-body spectrum. These states are identified as nearly degenerate resonant pairs, well captured by an analytical ansatz. Remarkably, such atypical eigenstates persist even at very strong disorder, a regime in which conventional diagnostics suggest robust localization. These results offer fresh insight into the MBL problem and reopen fundamental questions about the mechanisms that might destabilize the MBL phase.