Equilibrium Dynamics of the Dissipative Two-State System

Wilson's momentum shell renormalization group method is used to solve for the dynamics of the dissipative two-state system. We utilize the mapping of the spin-boson model onto the anisotropic Kondo model (AKM) and solve for the dynamics of the latter. We find that the AKM captures the physics of the dissipative two-state system for dissipation strength $0\le \alpha \le 4$ corresponding to $\infty \ge J_{\Vert }\ge -\infty$ in the AKM. The dynamics of the AKM shows a smooth crossover between two strong coupling regimes corresponding to weak and strong dissipation in the spin-boson model.