Scaling feature of magnetic field induced Kondo-peak splittings

Abstract

By using the full density matrix approach to spectral functions within the numerical renormalization group method, we present a detailed study of the magnetic field induced splittings in the spin-resolved and the total spectral densities of a Kondo correlated quantum dot described by the single level Anderson impurity model. The universal scaling of the splittings with magnetic field is examined by varying the Kondo scale either by a change of local level position at a fixed tunnel coupling or by a change of the tunnel coupling at a fixed level position. We find that the Kondo-peak splitting $\ensuremath{\Delta}/{T}_{K}$ in the spin-resolved spectral function always scales perfectly for magnetic fields $B<8{T}_{K}$ in either of the two ${T}_{K}$-adjusted paths. Scaling is destroyed for fields $B>10{T}_{K}$. On the other hand, the Kondo peak splitting $\ensuremath{\delta}/{T}_{K}$ in the total spectral function does slightly deviate from the conventional scaling theory in whole magnetic field window along the coupling-varying path. Furthermore, we show the scaling analysis suitable for all field windows within the Kondo regime and two specific fitting scaling curves are given from which certain detailed features at low field are derived. In addition, the scaling dimensionless quantity $\ensuremath{\Delta}/2B$ and $\ensuremath{\delta}/2B$ are also studied and they can reach and exceed 1 in the large magnetic field region, in agreement with a recent experiment [T. M. Liu et al., Phys. Rev. Lett. 103, 026803 (2009)].