Various time evolution methods have been developed , including direct evolution and compression, time step-targeting, time-dependent variational principle, and so on. In this work, we adopt the time-dependent variational principle with projector-splitting algorithm (TDVP-PS) for time evolution, which has been proved efficient and robust, especially with the hybrid CPU-GPU heterogeneous algorithms . The basic idea of TDVP-PS is projecting 𝐻𝐻 � |Ψ⟩ onto the tangent space of current MPS via projection operator 𝑃𝑃 � :