The results obtained during this reporting period are beyond the state of the art. In particular, numerical simulations of the dynamics of many-body localized systems used parallel algorithm and achieved very large bond dimensions needed to capture the large entanglement present in the system. Moreover, we developed new analytical and numerical techniques to address the properties of quantum many-body scars, based on tensor networks and algebraic methods.
Towards the end of the 5 year period we expect to have an advanced method toolbox for accessing eigenstates, dynamics, and controlling non-ergodic systems.