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 an 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 confirms the 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.

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• Nonequilibrium statistical mechanics
• Open quantum systems
• Nonequilibrium systems
• Matrix product states
• Tensor network renormalization