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

Signatures of Dissipation Driven Quantum Phase Transition in Rabi Model