Topological quantum phase transition between Fermi liquid phases in an Anderson impurity model

We study a generalized Anderson model that mixes two localized configurations –one formed by two degenerate doublets and the other by a triplet with single-ion anisotropy $D{S}_z^2$– by means of two degenerate conduction channels. The model has been derived for a single Ni impurity embedded into an O-doped Au chain. Using the numerical renormalization group, we find a topological quantum phase transition, at a finite value $D_c,$ between two regular Fermi liquid phases of high (low) conductance and topological number $2 I_L/\pi = 0$(-1)for$D < D_c$($D > D_c$),where$I_L$ is the well-known Luttinger integral. At finite temperature the two phases are separated by a non-Fermi liquid phase with fractional impurity entropy $\frac{1}{2}\mathrm{l}\mathrm{n}2$ and other properties which remind those of the two-channel Kondo model.