Fixed point annihilation for a spin in a fluctuating field

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'|(-(2-8)). 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.

Automated summary

In this study, it is shown that the quantum spin impurity coupled to a gapless free field exhibits an annihilation between two nontrivial renormalization group fixed points at a critical value of the interaction exponent. This clarifies the phase diagram of the Bose-Kondo model and highlights its role as a toy model for fixed point annihilation and quasiuniversality in higher dimensions.