  By using worldline Monte Carlo technique, matrix product state and a
variational approach \`a la Feynman, we investigate the equilibrium properties
and relaxation features of the dissipative quantum Rabi model, where a two
level system is coupled to a linear harmonic oscillator embedded in a viscous
fluid. We show that, in the Ohmic regime, a Beretzinski-Kosterlitz-Thouless
quantum phase transition occurs by varying the coupling strength between the
two level system and the oscillator. This is a non perturbative result,
occurring even for extremely low dissipation magnitude. By using
state-of-the-art theoretical methods, we unveil the features of the relaxation
towards the thermodynamic equilibrium, pointing out the signatures of quantum
phase transition both in the time and frequency domains. We prove that, for low
and moderate values of the dissipation, the quantum phase transition occurs in
the deep strong coupling regime. We propose to realize this model by coupling a
flux qubit and a damped LC oscillator.
