Flow equations for the spin-boson problem

摘要: Using continuous unitary transformations recently introduced by Wegner [1], we obtain flow equations for the parameters of spin-boson Hamiltonian. Interactions not contained in original Hamiltonian are generated this transformation. Within an approximation that neglects additional interactions quadratic bath operators, can close equations. Applying formalism to case Ohmic dissipation at zero temperature, calculate renormalized tunneling frequency. We find a transition from untrapped trapped state critical coupling constant αc=1. also static susceptibility via equilibrium spin correlation function. Our results both consistent with known Kondo problem and those obtained mode-coupling theories. finite coherent incoherent atT2*≈2T1*, whereT1* is crossover temperature dynamics NIBA.