Local quantum critical behavior in magnetic Kondo impurity models with partially screened moment

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In the strong coupling limit, an effective resonant level model is derived for the spin-1 underscreened Kondo impurity model. A local quantum critical behavior is induced by the formation of a bound state with partially screened magnetic moment, displaying a residual Z₂ symmetry, leading to a δ-resonance at the Fermi level in the impurity spectral function. As a consequence, a logarithmic singularity appears in the real part of the impurity dynamic spin susceptibility as a function of (ω, T), with ω as frequency, T temperature. A small magnetic field breaks this Z₂ symmetry and suppresses the singularity. We also discuss the possible manifestation of such a quantum critical behavior in the spin-1/2 two Kondo impurity model and the single quantum dot system with even electron occupation.