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 formulating with the original orbital basis as the Hamiltonian, enables detailed studies of the sub-Kondo spectral evolution in the zero-temperature limit, confirming the double-resonance structure at bias of the Kondo energy scale $T_K$. The distribution shows distinct multi-scale spectral features at energy $\omega$ below the Kondo scale ($\omega\lesssim T_K$) and near the bias ($\omega\gtrsim V$), leading to the nonequilibrium temperature $T_{\rm loc}$ local to the Kondo dot scaling as $k_BT_{\rm loc}\approx V$ for $V\gg T_K$. The current-voltage relation in the low-temperature limit ($T\ll T_K$) deviates from the unitary limit as the bias exceeds the Kondo scale ($V/2\gtrsim T_K$) and reaches the current saturation regime.