  We study the breaking of ergodicity measured in terms of return probability
in the evolution of a quantum state of a spin chain. In the non ergodic phase a
quantum state evolves in a much smaller fraction of the Hilbert space than
would be allowed by the conservation of extensive observables. By the anomalous
scaling of the participation ratios with system size we are led to consider the
distribution of the wave function coefficients, a standard observable in modern
studies of Anderson localization. We finally present a criterion for the
identification of the ergodicity breaking (many-body localization) transition
based on these distributions which is quite robust and well suited for
numerical investigations of a broad class of problems.
