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Transition between SU(4) and SU(2) Kondo effect

Motivated by experiments in nanoscopic systems, we study a generalized Anderson, which consists of two spin degenerate doublets hybridized to a singlet by promotion of an electron to two conduction bands, as a function of the energy separation $δ$ between both doublets. For $δ$=0 or very large, the model is equivalent to a one-level SU(N) Anderson model, with N=4 and 2 respectively. We study the evolution of the spectral density for both doublets ($ρ_{1 σ}(ω)$ and $ρ_{2 σ}(ω)$) and their width in the Kondo limit as $δ$ is varied, using the non-crossing approximation (NCA). As $δ$ increases, the peak at the Fermi energy in the spectral density (Kondo peak) splits and the density of the doublet of higher energy $ρ_{2 σ}(ω)$ shifts above the Ferrmi energy. The Kondo temperature $T_K$ (determined by the half width at half maximum of the Kondo peak in density of the doublet of lower energy $ρ_{1 σ}(ω)$) decreases dramatically. The variation of $T_K$ with $δ$ is reproduced by a simple variational calculation.