Title: Reduced-basis approach to many-body localization,
Abstract: Within the standard model of many-body localization, i.e., the disordered
chain of spinless fermions, we investigate how the interaction affects the
many-body states in the basis of noninteracting localized Anderson states. From
this starting point we follow the approach that uses a reduced basis of
many-body states. Together with an extrapolation to the full basis, it proves
to be efficient for the evaluation of the stiffnesses of local observables,
which remain finite within the non-ergodic regime and represent the hallmark of
the many-body localization (MBL). The method enables a larger span of system
sizes and, within the MBL regime, allows for a more careful analysis of the
size scaling of calculated quantities. On the other hand, the survival
stiffness as the representative of non--local quantities, reveals limitations
of the reduced-basis approach.