Zeitschrift für Physik B Condensed Matter

, Volume 99, Issue 2, pp 269–280 | Cite as

Flow equations for the spin-boson problem

  • Stefan K. Kehrein
  • Andreas Mielke
  • Peter Neu
Original Contributions


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


71.10+X 05.30.Jp 71.38.+ 


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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Stefan K. Kehrein
    • 1
  • Andreas Mielke
    • 1
  • Peter Neu
    • 1
  1. 1.Institut für Theoretische PhysikRuprecht-Karls-UniversitätHeidelbergGermany

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