Nonequilibrium Statistics of Biased Kondo Resonance

Numerical renormalization group (NRG) is formulated for nonequilibrium steady-state by converting finite-lattice many-body eigenstates into scattering states. Extension of the full-density-matrix NRG for a biased Anderson impurity model, simplified by using the original orbital basis of the Hamiltonian, enables detailed studies of the sub-Kondo spectral evolution in the zero-temperature limit, confirming the double-resonance structure emerging at bias $V$ equal to the Kondo energy scale $T_K$. The distribution shows distinct multi-scale spectral features of population inversion at energy $\omega$ below the Kondo scale ($\omega\lesssim T_K$) and very strong nonequilibrium excitations at energy beyond the bias ($\omega\gtrsim V$). The strong departure from the Fermi-Dirac distribution leads to the local nonequilibrium temperature $T_{\rm loc}$ scaling as $k_BT_{\rm loc}\approx V$ for $V\gg T_K$. The current-voltage relation at the low-temperatures ($T\ll T_K$) in the Kondo regime evolves from the unitary limit to the current saturation regime as the bias increases from zero to beyond the Kondo scale.