Quantum critical point between two-channel Kondo and Fermi-liquid phases

We investigate the emergence of quantum critical points near a two-channel Kondo phase by evaluating an f-electron entropy of a seven-orbital impurity Anderson model hybridized with three (Γ₇ and Γ₈) conduction bands with the use of a numerical renormalization group method. First we consider the case of Pr³⁺ ion, in which quadrupole two-channel Kondo effect is known to occur for the local Γ₃ doublet state. When we control crystalline electric field (CEF) potentials so as to change the local CEF ground state from Γ₃ doublet to Γ₁ singlet or Γ₅ triplet, we commonly observe a residual entropy of log ϕ with the golden ratio ϕ = (1 + √5)/2, which is equal to that for three-channel Kondo effect. This peculiar residual entropy is also observed for the case of Nd³⁺ ion, in which magnetic two-channel Kondo phase is found to occur for the local Γ₆ doublet state. We envisage a scenario that the quantum critical point characterized by log ϕ generally appears between two-channel Kondo and Fermi-liquid phases. (author)