Width of the charge-transfer peak in the SU(N) impurity Anderson model and its relevance to non-equilibrium transport

We calculate the width \(2\Delta_{\text{CT}}\) and intensity of the charge-transfer peak (the one lying at the on-site energy \(E_d\)) in the impurity spectral density of states as a function of \(E_d\) in the SU(\(N\)) impurity Anderson model (IAM). We use the dynamical density-matrix renormalization group (DDMRG) and the noncrossing-approximation (NCA) for \(N\)=4, and a 1/\(N\) variational approximation in the general case. In particular, while for \(E_d \gg \Delta\), where \(\Delta\) is the resonant level half-width, \(\Delta_{\text{CT}}=\Delta\) as expected in the noninteracting case, for \(-E_d \gg N \Delta\) one has \(\Delta_{\text{CT}}=N\Delta\). In the \(N\)=2 case, some effects of the variation of \(% \Delta_{\text{CT}}\) with \(E_d\) were observed in the conductance through a quantum dot connected asymmetrically to conducting leads at finite bias [J. K\"onemann \textit{et al.}, Phys. Rev. B \textbf{73}, 033313 (2006)]. More dramatic effects are expected in similar experiments, that can be carried out in systems of two quantum dots, carbon nanotubes or other, realizing the SU(4) IAM.