Single mode approximation for sub-Ohmic spin-boson model: adiabatic limit and critical properties
Department of Physics, Renmin University of
Received in final form: 11 February 2013
Published online: 8 April 2013
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 αc, 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 αc as the mean-field approximation. The critical exponents are classical: β = 1/2, δ = 3, γ = 1, x = 1/2, yt∗ = 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.
Key words: Computational Methods
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013