Quantum phase transition of many interacting spins coupled to a bosonic bath: Static and dynamical properties

By using worldline and diagrammatic quantum Monte Carlo techniques, matrix product state, and a variational approach à 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 α. We show that, in the Ohmic regime, a Beretzinski-Thouless-Kosterlitz quantum phase transition occurs. While for J=0 the critical value of α 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 α 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 à la Feynman jointly, we unveil the features of the relaxation, that, in particular, exhibits a nonmonotonic 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.