Annales Henri Poincaré

, Volume 12, Issue 4, pp 621-677

First online:

Ground States in the Spin Boson Model

  • David HaslerAffiliated withDepartment of Mathematics, College of William and Mary Email author 
  • , Ira HerbstAffiliated withDepartment of Mathematics, University of Virginia


We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant λ. We show that the ground-state energy is an analytic function of λ and that the corresponding ground state can also be chosen to be an analytic function of λ. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground-state energy can be calculated using regular analytic perturbation theory.