  We proposed and theoretically studied a model of two separated spins coupled
to a common bosonic bath. In our SU(2)-symmetric model, the phase transition
point and the stable fixed point representing the nonclassical phase can be
continuously tuned by the distance between the two spins. Thus the fixed point
collision and annihilation (FPCAA) could be achieved by simply changing the
distance. Moreover, we studied in detail variation of the critical value when
the distance is changed. Finally, we also discussed several possible
generalizations of our model which may be worth further studying. Our work is
essential for realization of FPCAA in such systems and paves the way for
studying related physics such as deconfined criticality and quasiuniversality.
