  We study the two-orbital Hubbard model in the limit of vanishing kinetic
energy. The phase diagram in the $V-J$ plane, with $V$ and $J$ denoting the
interorbital hybridization and exchange coupling respectively, at half filling
is obtained. A singlet(dimer)-triplet transition is found for a critical value
of the ratio $V/J.$ The entropy of formation, both in the mode and in the
particle picture, presents a jump as the same critical line in conformity with
the suggested relation between criticality and entanglement.
