  We introduce the numerical linked cluster (NLC) expansion as a controlled
numerical tool for the study of the many-body localization (MBL) transition in
a disordered system with continuous non-perturbative disorder. Our approach
works directly in the thermodynamic limit, in any spatial dimension, and does
not rely on any finite size scaling procedure. We study the onset of many-body
delocalization through the breakdown of area-law entanglement in a generic
many-body eigenstate. By looking for initial signs of an instability of the
localized phase, we obtain a value for the critical disorder, which we believe
should be a lower bound for the true value, that is higher than current best
estimates from finite size studies. This implies that most current methods tend
to overestimate the extent of the localized phase due to finite size effects
making the localized phase appear stable at small length scales. We also study
the mobility edge in these systems as a function of energy density, and find
that our conclusion is the same at all examined energies.
