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

We calculate the width $2{\mathrm{\Delta }}_{\text{CT}}$ 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 $E_d\gg \mathrm{\Delta }$, where $\mathrm{\Delta }$ is the resonant level half-width, ${\mathrm{\Delta }}_{\text{CT}}=\mathrm{\Delta }$ as expected in the noninteracting case, for $-E_d\gg N\mathrm{\Delta }$ one has ${\mathrm{\Delta }}_{\text{CT}}=N\mathrm{\Delta }$. In the $N$=2 case, some effects of the variation of $$ with $E_d$ were observed in the conductance through a quantum dot connected asymmetrically to conducting leads at finite bias [J. K"onemann $\mathit{\text{et}}\mathit{\text{al.}}$, Phys. Rev. B $\mathbf{\text{73}}$, 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.