  The analytical solution of a many-body localization problem in a quantum
Sherrington-Kirkpatrick spin glass model in a random longitudinal field is
proposed matching the problem with a model of Anderson localization in a Bethe
lattice. The localization transition is dramatically sensitive to the
relationship between interspin interaction and random field revealing different
regimes in which the interaction can either suppress or enhance the
delocalization. The localization is enhanced by decreasing the temperature and
the localization transition shows a remarkable universality in a spin glass
phase. The observed trends should be qualitatively relevant for other systems
showing many-body localization.
