  We use the slave-spin mean-field approach to study particle-hole symmetric
one- and two-band Hubbard models in presence of Hund's coupling interaction. By
analytical analysis of Hamiltonian, we show that the locking of the two
orbitals vs.\,orbital-selective Mott transition can be formulated within a
Landau-Ginzburg framework. By applying the slave-spin mean-field to impurity
problem, we are able to make a correspondence between impurity and lattice. We
also consider the stability of the orbital selective Mott phase to the
hybridization between the orbitals and study the limitations of the slave-spin
method for treating inter-orbital tunnellings in the case of multi-orbital
Bethe lattices with particle-hole symmetry.
