Dynamics of the two-spin spin-boson model with a common bath

Dynamics of the two-spin spin-boson model in the presence of Ohmic and sub-Ohmic baths is investigated by employing a multitude of the Davydov D₁ trial states, also known as the multi-D₁ Ansatz. Its accuracy in dynamics simulations of the two-spin SBM is improved significantly over the single D₁ Ansatz, especially in the weak to moderately strong coupling regime. Validity of the multi-D₁ Ansatz for various coupling strengths is also systematically examined by making use of the deviation vector which quantifies how faithfully the trial state obeys the Schrödinger equation. The time evolution of population difference and entanglement has been studied for various initial conditions and coupling strengths. Careful comparisons are carried out between our approach and three other methods, i.e., the time-dependent numerical renormalization group (TD-NRG) approach, the Bloch-Redfield theory, and a method based on a variational master equation. For strong coupling, the multi-D₁ trial state yields consistent results as the TD-NRG approach in the Ohmic regime while the two disagree in the sub-Ohmic regime, where the multi-D₁ trial state is shown to be more accurate. For weak coupling, the multi-D₁ trial state agrees with the two master-equation methods in the presence of both Ohmic and sub-Ohmic baths, but shows considerable differences with the TD-NRG approach in the presence of a sub-Ohmic bath, calling into question the validity of the TD-NRG results at long times in the literature.