We study a generalized Anderson model proposed before for Ni impurities in O doped Au chains [1], that mixes two localized configurations, one formed by two degenerate doublets (a hole in either the Ni xz or yz orbital) and the other by a triplet with single-ion anisotropy D (Sz)² —by means of two degenerate conduction channels (Au xz and yz bands).

Using the numerical renormalization group, we have found [2] a topological quantum phase transition, at a finite value D = Dc , between two regular Fermi liquid phases.

For D < Dc the phase corresponds to compensated Kondo system with ordinary Fermi liquid behavior and high conductance at zero temperature.

For D > Dc the zero-temperature conductance is small and the Friedel sum rule has to be generalized to invoke a non-zero topological value of the Luttinger integral. The system is a non-Landau Fermi liquid state in the sense that it cannot be adiabatically connected to a non-interacting system. At finite temperature the two phases are separated by a non-Fermi liquid phase with similar properties to those of the two-channel Kondo model.

For negative D the physics is similar to an effective Kondo model, which mixes the two remaining degenerate states through a fourth-order term in the hybridization, with a Kondo temperature that scales exponentially with D².

[1] S. Di Napoli et al., Phys. Rev. B 92, 085120 (2015).

[2] G. G. Blesio et al., Phys. Rev. B 98, 195435 (2018).