We demonstrate that a boundary defect in the single spin-$\frac{1}{2}$ quantum XX chain exhibits two-channel Kondo physics. Due to the presence of the defect, the edge spin fractionalizes into two Majorana fermions, out of which one decouples, and one is overscreened by the free fermion in bulk, leading to nontrivial boundary behavior characteristic of the two-channel Kondo model. When the boundary-to-bulk coupling ratio exceeds a critical value of $\sqrt{2}$, a massive boundary-bound mode is exponentially localized near the impurity site for strong impurity coupling. This leads to unusual behavior in physical quantities, such as the $g$ function not being monotonic. We compute the $g$ function of the impurity from thermodynamic and entanglement entropy calculations and show that it takes a noninteger value of $\sqrt{2}$ just as in the two-channel Kondo problem.

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• Density matrix renormalization group
• Kondo effect
• Bethe ansatz
• Conformal field theory
• Exact diagonalization