We use the slave-spin mean-field approach to study particle-hole symmetric one- and two-band Hubbard models in presence of Hunds 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.
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