  We study the dynamical simulation of open quantum spin chain with nearest
neighboring coupling, where each spin in the chain is associated with a
harmonic bath. This is an extension of our previous work [G. Wang and Z. Cai,
J. Chem. Theory Comput., 19, 8523--8540, 2023] by generalizing the application
of the inchworm method and the technique of modular path integrals from
diagonally coupled cases to off-diagonally coupled cases. Additionally, to
reduce computational and memory cost in long time simulation, we apply
tensor-train representation to efficiently represent the reduced density matrix
of the spin chains, and employ the transfer tensor method (TTM) to avoid
exponential growth of computational cost with respect to time. Abundant
numerical experiments are performed to validate our method.
