  It is shown that a minimum realization of the dynamical mean-field theory
(DMFT) can be achieved by mapping a correlated lattice model onto an impurity
model in which the impurity is coupled to an uncorrelated bath that consists of
a single site only. The two-site impurity model can be solved exactly. The
mapping is approximate. The self-consistency conditions are constructed in a
way that the resulting ``two-site DMFT'' reduces to the previously discussed
linearized DMFT for the Mott transition. It is demonstrated that a reasonable
description of the mean-field physics is possible with a minimum computational
effort. This qualifies the simple two-site DMFT for a systematic study of more
complex lattice models which cannot be treated by the full DMFT in a feasible
way. To show the strengths and limitations of the new approach, the single-band
Hubbard model is investigated in detail. The predictions of the two-site DMFT
are compared with results of the full DMFT. Internal consistency checks are
performed which concern the Luttinger sum rule, other Fermi-liquid relations
and thermodynamic consistency.
