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Single mode approximation for sub-Ohmic spin-boson model: adiabatic limit and critical properties

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  • Fei-Ran Liu
  • Ning-Hua Tong

Abstract

In this work, we study the quantum phase transition in the sub-Ohmic spin-boson model using a single-mode approximation. It combines the rotating wave transformation and the transformations used in the numerical renormalization group (NRG). Analytical results for the critical coupling strength α c , the magnetic susceptibility χ(T), and the spin-spin correlation function C(ω) at finite temperatures are obtained and further confirmed by numerical results. We obtain the same α c as the mean-field approximation. The critical exponents are classical: β = 1/2, δ = 3, γ = 1, x = 1/2, y t ∗ =1/2, in agreement with the spin-boson model in 0 > s > 1/2 regime. C(ω) has nontrivial behavior reflecting coherent oscillation with temperature dependent damping effects due to the environment. We point out that the original NRG has a problem with the crossover temperature T ∗ , and propose a chain Hamiltonian possibly suitable for implementing NRG without boson state truncation error. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Fei-Ran Liu & Ning-Hua Tong, 2013. "Single mode approximation for sub-Ohmic spin-boson model: adiabatic limit and critical properties," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(4), pages 1-11, April.
    • Handle: RePEc:spr:eurphb:v:86:y:2013:i:4:p:1-11:10.1140/epjb/e2013-31100-y
    DOI: 10.1140/epjb/e2013-31100-y
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