  A fast time propagation method for nonequilibrium Green's functions based on
the generalized Kadanoff--Baym Ansatz (GKBA) is applied to a lattice system
with a symmetry-broken equilibrium phase, namely an excitonic insulator. The
adiabatic preparation of a correlated symmetry-broken initial state from a
Hartree--Fock wave function within GKBA is assessed by comparing with a
solution of the imaginary-time Dyson equation. We find that it is possible to
reach a symmetry-broken correlated initial state with nonzero excitonic order
parameter by the adiabatic switching procedure. We discuss under which
circumstances this is possible in practice within reasonably short switching
times.
