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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 iscoupled to a non-interacting conduction band. The system corresponds to animpurity Anderson model in which the conduction band has a Lorentzian densityof 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 inrho(omega) splits into two peaks. This splitting can be understood in terms ofweakly interacting quasiparticles. Before the splitting takes place theuniversal properties of the model in the Kondo regime are lost. Using theSBMFA, simple analytical expressions for the occurrence of split peaks areobtained. For small or moderate Delta2, the side bands of rho(omega) have theform of narrow resonances, that were missed in previous studies using thenumerical renormalization group. This technique also has shortcomings fordescribing properly the split Kondo peaks. As the temperature is increased, theintensity of the split Kondo peaks decreases, but it is not completelysuppressed at high temperatures.

Spectral density of an interacting dot coupled indirectly to conducting leads