Polarization dynamics of the spin-boson model in the shifted boson Hilbert space

Faithfully simulating the dynamics of open quantum systems requires efficiently addressing the challenge of an infinite Hilbert space. Inspired by the shifted boson operator technique used in ground-state studies of the spin-boson model (SBM), we develop a novel algorithm that integrates a shifted optimized boson basis with the time-evolving block decimation method. We validate our approach by accurately reproducing the polarization dynamics of the sub-Ohmic SBM at a significantly reduced computational cost. For the Ohmic SBM, we demonstrate that the time-evolved final state converges precisely to the variational prediction at both zero and finite temperatures. Furthermore, our method reveals a new aperiodic pseudocoherent phase in the super-Ohmic SBM with an initially polarized bath. This work establishes an efficient and powerful approach for simulating the real-time dynamics of open quantum systems.