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We derive an exact operatorial reformulation of the rotational invariant slave boson method and we apply it to describe the orbital differentiation in strongly correlated electron systems starting from first principles. The approach enables us to treat strong electron correlations, spin-orbit coupling and crystal field splittings on the same footing by exploiting the gauge invariance of the mean-field equations. We apply our theory to the archetypical nuclear fuel UO$_2$, and show that the ground state of this system displays a pronounced orbital differention within the $5f$ manifold, with Mott localized $Gamma_8$ and extended $Gamma_7$ electrons.
Motivated by the anomalous temperature dependence of the c-axis resistivity of Sr$_2$RuO$_4$, the dimensional crossover from a network of perpendicular one-dimensional chains to a two-dimensional system due to a weak hybridization between the perpend
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-sel
Using a rotationally invariant version of the slave-boson approach in spin space we analyze the stability of stripe phases with large unit cells in the two-dimensional Hubbard model. This approach allows one to treat strong electron correlations in t
A method to calculate the crystal field parameters {it ab initio} is proposed and applied to trivalent rare earth impurities in yttrium aluminate and to Tb$^{3+}$ ion in TbAlO$_3$. To determine crystal field parameters local Hamiltonian expressed in
Nonresonant inelastic x-ray scattering (NIXS) has been performed on single crystals of UO$_2$ to study the direction dependence of higher-order-multipole scattering from the uranium $O_{4,5}$ edges (90--110 eV). By comparing the experimental results