  By using worldline and diagrammatic quantum Monte Carlo techniques, matrix
product state and a variational approach \`a la Feynman, we investigate the
equilibrium properties and relaxation features of a quantum system of $N$ spins
antiferromagnetically interacting with each other, with strength $J$, and
coupled to a common bath of bosonic oscillators, with strength $\alpha$. We
show that, in the Ohmic regime, a Beretzinski-Thouless-Kosterlitz quantum phase
transition occurs. While for $J=0$ the critical value of $\alpha$ decreases
asymptotically with $1/N$ by increasing $N$, for nonvanishing $J$ it turns out
to be practically independent on $N$, allowing to identify a finite range of
values of $\alpha$ where spin phase coherence is preserved also for large $N$.
Then, by using matrix product state simulations, and the Mori formalism and the
variational approach \`a la Feynman jointly, we unveil the features of the
relaxation, that, in particular, exhibits a non monotonic dependence on the
temperature reminiscent of the Kondo effect. For the observed quantum phase
transition we also establish a criterion analogous to that of the
metal-insulator transition in solids.
