  We comparatively study the excitonic insulator state in the extended
Falicov-Kimball model (EFKM, a spinless two-band model) on the two-dimensional
square lattice using the variational cluster approximation (VCA) and the
cluster dynamical impurity approximation (CDIA). In the latter, the
particle-bath sites are included in the reference cluster to take into account
the particle-number fluctuations in the correlation sites. We thus calculate
the particle-number distribution, order parameter, ground-state phase diagram,
anomalous Green's function, and pair coherence length, thereby demonstrating
the usefulness of the CDIA in the discussion of the excitonic condensation in
the EFKM.
