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We use the slave-spin mean-field approach to study particle-hole symmetricone- and two-band Hubbard models in presence of Hund's coupling interaction. Byanalytical analysis of Hamiltonian, we show that the locking of the twoorbitals vs.\,orbital-selective Mott transition can be formulated within aLandau-Ginzburg framework. By applying the slave-spin mean-field to impurityproblem, we are able to make a correspondence between impurity and lattice. Wealso consider the stability of the orbital selective Mott phase to thehybridization between the orbitals and study the limitations of the slave-spinmethod for treating inter-orbital tunnellings in the case of multi-orbitalBethe lattices with particle-hole symmetry.

Analytical slave-spin mean-field approach to orbital selective Mott insulators