Annales Henri Poincaré

, Volume 12, Issue 4, pp 621–677

Ground States in the Spin Boson Model


    • Department of MathematicsCollege of William and Mary
  • Ira Herbst
    • Department of MathematicsUniversity of Virginia

DOI: 10.1007/s00023-011-0091-6

Cite this article as:
Hasler, D. & Herbst, I. Ann. Henri Poincaré (2011) 12: 621. doi:10.1007/s00023-011-0091-6


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.

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© Springer Basel AG 2011