  DMFT combined with finite-T exact diagonalization is one of the methods to
describe electronic properties of strongly correlated materials. Because of the
rapid growth of the Hilbert space, the size of the finite bath used to
represent the infinite lattice is severely limited. In view of the increasing
interest in the effect of multi-orbital and multi-site Coulomb correlations in
transition metal oxides, high-Tc cuprates, iron-based pnictides, organic
crystals, etc., it is appropriate to explore the range of temperatures and bath
sizes in which ED provides accurate results for various system properties. The
bath must be large enough to achieve a sufficiently dense level spacing, so
that useful spectral information can be derived, especially close to the
Fermi-level. For an adequate projection of the lattice Green's function onto a
finite bath, the choice of the temperature is crucial. The role of these two
key ingredients in ED DMFT is discussed for a wide variety of systems in order
to establish the domain of applicability of this approach. Three criteria are
used to illustrate the accuracy of the results: (i) the convergence of the
self-energy with bath size, (ii) quality of the discretization of the bath
Green's function, and (iii) comparisons with complementary results obtained via
CTQMC DMFT. The materials comprise a variety of three- and five-orbital
systems, as well as single-band Hubbard models for two-dimensional triangular,
square and honeycomb lattices, where non-local Coulomb correlations are
important. The main conclusion from these examples is that a larger number of
correlated orbitals or sites requires a smaller number of bath levels. Down to
temperatures of 5 to 10 meV (for typical band widths W=2 eV) two bath levels
per correlated impurity orbital or site are usually adequate.
