Long-range resonances and the meltdown of many-body localization*

Closed, quantum systems with interactions can transition to a many-body localized (MBL) phase in the presence of disorder. In this work, we attempt to numerically identify the presence of resonances in the ergodic-MBL transition. We find evidence for the proliferation of resonances around the transition, where the resonance structure becomes scale invariant. In addition, we consider how the resonances induce the buildup of entanglement and spectral statistics observed in the system through collisions between energy levels. We explore this both in the real-space basis as well as an adiabatic l-bit basis.