We study the spectral density of electrons rho in an interacting quantum dot (QD) with a hybridization lambda to a non-interacting QD, which in turn is coupled to a non-interacting conduction band. The system corresponds to an impurity Anderson model in which the conduction band has a Lorentzian density of states of width Delta2. We solved the model using perturbation theory in the Coulomb repulsion U (PTU) up to second order and a slave-boson mean-field approximation (SBMFA). The PTU works surprisingly well near the exactly solvable limit Delta2 -> 0. For fixed U and large enough lambda or small enough Delta2, the Kondo peak in rho(omega) splits into two peaks. This splitting can be understood in terms of weakly interacting quasiparticles. Before the splitting takes place the universal properties of the model in the Kondo regime are lost. Using the SBMFA, simple analytical expressions for the occurrence of split peaks are obtained. For small or moderate Delta2, the side bands of rho(omega) have the form of narrow resonances, that were missed in previous studies using the numerical renormalization group. This technique also has shortcomings for describing properly the split Kondo peaks. As the temperature is increased, the intensity of the split Kondo peaks decreases, but it is not completely suppressed at high temperatures.
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