  The annihilation of two intermediate-coupling renormalization-group (RG)
fixed points is of interest in diverse fields from statistical mechanics to
high-energy physics, but has so far only been studied using perturbative
techniques. Here we present high-accuracy quantum Monte Carlo results for the
SU(2)-symmetric $S=1/2$ spin-boson (or Bose-Kondo) model. We study the model
with a power-law bath spectrum $\propto \omega^s$ where, in addition to a
critical phase predicted by perturbative RG, a stable strong-coupling phase is
present. Using a detailed scaling analysis, we provide direct numerical
evidence for the collision and annihilation of two RG fixed points at $s^\ast =
0.6540(2)$, causing the critical phase to disappear for $s<s^\ast$. In
particular, we uncover a surprising duality between the two fixed points,
corresponding to a reflection symmetry of the RG beta function, which we
utilize to make analytical predictions at strong coupling which are in
excellent agreement with numerics. Our work makes phenomena of fixed-point
annihilation accessible to large-scale simulations, and we comment on the
consequences for impurity moments in critical magnets.
