  Although the mathematics of anyon condensation in topological phases has been
studied intensively in recent years, a proof of its physical existence is
tantamount to constructing an effective Hamiltonian theory. In this paper, we
concretely establish the physical foundation of anyon condensation by building
the effective Hamiltonian and the Hilbert space, in which we explicitly
construct the vacuum of the condensed phase as the coherent states that are the
eigenstates of the creation operators that create the condensate anyons. Along
with this construction, which is analogous to Laughlin's construction of
wavefunctions of fractional quantum hall states, we generalize the Goldstone
theorem in the usual spontaneous symmetry breaking paradigm to the case of
anyon condensation. We then prove that the condensed phase is a symmetry
enriched (protected) topological phase by directly constructing the
corresponding symmetry transformations, which can be considered as a
generalization of the Bogoliubov transformation.
