Many-body localization (MBL) occurs in isolated quantum
systems when Anderson localization persists in the presence of finite
interactions. The MBL phase is characterized by a breakdown of ergodicity
and a slow entanglement growth following a quantum quench.
*First, we show that the quantum mutual information (QMI) between two
small, spatially separated regions is a useful probe to study many-body
localization (MBL). The QMI can in principle be used in an experimental
setup to detect the MBL transition and allows to distinguish between
an Anderson insulator and an MBL phase.
*Second, we study the effects of local perturbations on the dynamics of
disordered fermionic systems in order to characterize time-irreversibility.
We consider the dynamics of the full many-body wave-functions by measuring
the Loschmidt echo (LE) and find qualitatively different behavior in
localized and extended phases.