$\frac{1}{N}$ expansion of the nonequilibrium infinite-$U$ Anderson model

Results are presented for the nonequilibrium infinite-$U$ Anderson model using a large $N$ approach, where $N$ is the degeneracy of the impurity level, and where nonequilibrium is established by coupling the level to two leads at two different chemical potentials so that there is current flow. A slave-boson representation combined with Keldysh functional integral methods is employed. Expressions for the static spin susceptibility ${\chi }_S$ and the conductance $G$ are presented to $\mathcal{O}\left(\frac{1}{N}\right)$ and for an applied voltage difference $V$ less than the Kondo temperature. The correlation function for the slave boson is found to be significantly modified from its equilibrium form in that it acquires a rapid decay in time with a rate that equals the current-induced decoherence rate. Physical observables are found to have a rather complex dependence on the coupling strength to the two leads which can lead to asymmetric behavior ${\chi }_S\left(V\right)\ne {\chi }_S\left(-V\right)$, $G\left(V\right)\ne G\left(-V\right)$ both in the mixed valence and in the Kondo regime.

Figure 1

Diagrams representing the mean-field Green’s function ${\widehat{G}}_{\text{mf}}$, the self-energy due to coupling to leads ${\widehat{\Sigma }}_c$, and the bosonic propagator $\widehat{D}$. Each has a $2\times 2$ Keldysh structure.

Figure 2

The bosonic self-energies corresponding to (a) $\Pi$, (b) $\delta {\Pi }^{\left(1\right)}$, and (c). $\delta {\Pi }^{\left(2\right)}$ in text.

Figure 3

Diagram contributing to the $1/N$ correction to $n_F$.

Figure 4

Diagrams contributing to the susceptibility to $\mathcal{O}\left(1/N\right)$.

Figure 5

Diagrams needed for the computation of the impurity spectral density to $\mathcal{O}\left(1/N^2\right)$ and hence the conductance to $\mathcal{O}\left(1/N^2\right)$.

Figure 6

Fermionic self-energy.