  In this paper we propose a new perspective to analyze the many-body
localization (MBL) transition when recast in terms of a single-particle
tight-binding model in the space of many-body configurations. We compute the
distribution of tunneling rates between many-body states separated by an
extensive number of spin flips at the lowest order in perturbation theory
starting from the insulator, and determine the scaling of their typical
amplitude with the number of accessible states in the Hilbert space. By using
an analogy with the Rosenzweig-Porter random matrix ensemble, we propose an
ergodicity breaking criterion for the MBL transition based on the Fermi Golden
Rule. According to this criterion, in the MBL phase many resonances are formed
at large distance from an infinite temperature initial state, but they are not
enough for the quantum dynamics to decorrelate from it in a finite time. This
implies that, differently from Anderson localized states, in the insulating
phase many-body eigenstates are multifractal in the Hilbert space, as they
occupy a large but subexponential part of the total volume, in agreement with
recent numerical results, perturbative calculations, and intuitive arguments.
Possible limitations and implications of our interpretation are discussed in
the conclusions.
