Fixed point annihilation for a spin in a fluctuating field
Résumé
A quantum spin impurity coupled to a gapless free field (the Bose-Kondo model) can be represented as a -dimensional field theory with long-range-in-time interactions that decay as . This theory is a simpler analog of nonlinear 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 of the interaction exponent. The calculation is controlled at large spin . 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.