At which magnetic field, exactly, does the Kondo resonance begin to   split? A Fermi liquid description of the low-energy properties of the   Anderson model
  This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. --- We extend a recently-eveloped Fermi-liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora $et al.$, Phys. Rev. B, 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's low-lying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective low-energy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spin-dependent ground-state occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe Ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, $c_A$, describing its leading $\sim\varepsilon^2$ term, and the transport coefficients $c_V$ and $c_T$, describing the leading $\sim V^2$ and $\sim T^2$ terms in the nonlinear differential conductance. A sign change in $c_A$ or $c_V$ is indicative of a change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. We find that the fields $B_A$, $B_T$ and $B_V$ at which $c_A$, $c_T$ and $c_V$ change sign, respectively, are all of order $T_K$, as expected, with $B_A = B_T = B_V = 0.75073\,T_K$ in the Kondo limit. 
Michele Filippone, Catalin Pascu Moca, Andreas Weichselbaum, Jan von   Delft, Christophe Mora
cond-mat.mes-hall cond-mat.str-el