where σx and σz are the Pauli matrices, Î is a 2 × 2 identity matrix, R and P are the position and momentum operators of the boson mode. The parameter ζ controls the electronic-nuclear coupling, and ∆ is the electronic coupling between two electronic states. We choose 2∆ = ω = m = 1 and increasing values of the coupling strength parameter, the temperature is chosen in order to have β = 16. The initial electronic state is prepared on state |1 .