A quantum spin impurity coupled to a gapless free field (the Bose-Kondo model) can be represented as a $(0+1)$-dimensional field theory with long-range-in-time interactions that decay as $|t-t^{\prime }{|}^{-(2-\delta )}$. This theory is a simpler analog of nonlinear $\sigma$ models with topological Wess-Zumino-Witten terms in higher dimensions. In this Letter we show that the renormalization group (RG) flows for the impurity problem exhibit an annihilation between two nontrivial RG fixed points at a critical value ${\delta }_c$ of the interaction exponent. The calculation is controlled at large spin $S$. This clarifies the phase diagram of the Bose-Kondo model and shows that it serves as a toy model for phenomena involving fixed point annihilation and “quasiuniversality” in higher dimensions.

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• Kondo effect
• Nonlinear sigma model
• Spin dynamics
• Topological phases of matter
• 0-dimensional systems
• Heavy-fermion systems
• Kondo insulators
• Strongly correlated systems
• Conformal field theory
• Renormalization group
• Single impurity model
• Spin-boson model