  We show how exact diagonalization of small clusters can be used as a fast and
reliable impurity solver by determining the phase diagram and physical
properties of the bosonic single-impurity Anderson model. This is specially
important for applications which require the solution of a large number of
different single-impurity problems, such as the bosonic dynamical mean field
theory of disordered systems. In particular, we investigate the connection
between spontaneous global gauge symmetry breaking and the occurrence of
Bose-Einstein condensation (BEC). We show how BEC is accurately signaled by the
appearance of broken symmetry, even when a fairly modest number of states is
retained. The occurrence of symmetry breaking can be detected both by adding a
small conjugate field or, as in generic quantum critical points, by the
divergence of the associated phase susceptibility. Our results show excellent
agreement with the considerably more demanding numerical renormalization group
(NRG) method. We also investigate the mean impurity occupancy and its
fluctuations, identifying an asymmetry in their critical behavior across the
quantum phase transitions between BEC and `Mott' phases.
