where K = N sys (P + 1). An example of the MPS/TT decomposition of |Ψ(t) is shown schematically in Fig. ). Here, {A } are rank-3 tensors, with one index being either v i , v ′ i , or n α p , and the other two virtual indices r k-1 and r k corresponding the bond connecting the neighboring tensors. The virtual index r k runs from 1 to D k , where the bond dimension D k is a controllable parameter. The maximum value of {D k } is denoted as the maximal bond dimension D max . In practice, we systematically increase D max until the converged and numerically exact results are obtained. Similarly, the super-Hamiltonian H can be decomposed as the matrix product operator. For evolving Eq. ( ), we employ a time propagation scheme based on the time-dependent variational principle, as described in Refs. 45-47.