Equilibrium correlation functions of the spin-boson model with sub-Ohmic bath

Abstract

The spin-boson model is studied by means of flow equations for Hamiltonians. Our truncation scheme includes all coupling terms which are linear in the bosonic operators. Starting with the canonical generator η c =[ H 0, H] with H 0 resembling the non-interacting bosonic bath, the flow equations exhibit a universal attractor for the Hamiltonian flow. This allows to calculate equilibrium correlation functions for super-Ohmic, Ohmic and sub-Ohmic baths within a uniform framework including finite bias.