Figure 1

Zero-temperature transmission of an Anderson junction as a function of $\epsilon$ using Bethe ansatz (BA), Kohn-Sham DFT (KS), and (spin-restricted) Hartree-Fock (HF). As $U$ increases, HF misses the sharp structure, but the KS transport is always the same as that from BA.Reuse & Permissions

Figure 2

The occupancy of the Anderson junction as a function of $\mu -\epsilon$. The BA results (solid line) exhibit discrete charge steps when $U\gg \Gamma$, whereas the mean-field RHF (dashed line) never does. The approximate occupancies calculated self-consistently within the KS scheme using ${\tilde{\epsilon }}_{\mathrm{XC}}$ [Eq. (15)] (dotted line) are nearly indistinguishable from the BA results. The BA occupancies were used to generate Fig. 1.Reuse & Permissions

Figure 3

Transmission through an Anderson junction at fixed $\mu =3\mathrm{eV}$ with $\epsilon =0$, $\Gamma =0.5\mathrm{eV}$ and $U=10\mathrm{eV}$, so that $T_{\mathrm{K}}=2\mathrm{mK}$ [16, 17, 25]. The Doniach-Sunjic form [26] of the spectral function [27] is used near the Kondo peak, while the nonsingular portion is calculated using the methods of Refs. 5, 18 with the BA occupancy. Logarithmic shifts of the charging resonances are also included [25]. More sophisticated numerical methods [28] reproduce the qualitative features shown here.Reuse & Permissions

Figure 4

The KS potential ${\epsilon }^s$ of the Anderson junction. (a) For $U\approx \Gamma$, HF is accurate; as $U$ grows, an increasingly sharp step develops, due to the derivative discontinuity of the exchange-correlation energy as a function of particle number. (b) $\partial {\epsilon }^s/\partial ⟨n_C⟩$ for several large values of $U/\Gamma$. As $U/\Gamma \to \infty$, the exact (Lorentzian) asymptotic scaling form is recovered. (c) Exact and interpolated $\alpha$ and $\sigma$ functions are shown in the left and right-hand panels, respectively, showing the crossover from the mean-field ($U/\Gamma \sim 0$) to the strongly correlated regime ($U/\Gamma \to \infty$). The crossover from weakly to strongly correlated occurs for $U/\Gamma \approx 6$. (d) Exact and approximate $\partial {\epsilon }^s/\partial ⟨n_C⟩$ spectra for several moderate $U/\Gamma$ values, highlighting the accuracy of Eq. (15). The dashed lines use Eq. (16).Reuse & Permissions