The Kondo effect is an archetypical phenomenon in the physics of strongly
correlated electron systems. Recent attention has focused on the application of
Kondo physics to quantum information science by exploiting overscreened Kondo
impurities with residual anyon-like impurity entropy. While this physics was
proposed in the fine-tuned multi-channel Kondo setup or in the Majorana-based
topological Kondo effect, we here study the Kondo effect with symplectic
symmetry Sp(2k) and present details about the implementation which importantly
only involves conventional s-wave superconductivity coupled to an array of
resonant levels and neither requires perfect channel symmetry nor Majorana
fermions. We carefully discuss the role of perturbations and show that a global
Zeeman drives the system to a 2-channel SU(k) fixed point. Exact results for
the residual entropy, specific heat, and magnetization are derived using the
thermodynamic Bethe Ansatz for Sp(2k). This solution not only proves the
existence of a quantum critical ground state with anyon-like Hilbert space
dimension but also a particularly weak non-Fermi liquid behavior at
criticality. We interpret the weakness of non-analyticities as a manifestation
of suppressed density of states at the impurity causing only a very weak
connection of putative anyons and conduction electrons. Given this weak
connection, the simplicity of the design, and the stability of the effect, we
conjecture that the symplectic Kondo effect may be particularly suitable for
quantum information applications.

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