  Time dependent density matrix renormalization group (TD-DMRG) has become one
of the cutting edge methods of quantum dynamics for complex systems. In this
paper, we comparatively study the accuracy of three time evolution schemes in
TD-DMRG, the global propagation and compression method with Runge-Kutta
algorithm (P&C-RK), the time dependent variational principle based methods with
matrix unfolding algorithm (TDVPMU) and with projector-splitting algorithm
(TDVP-PS), by performing benchmarks on the exciton dynamics of
Fenna-Matthews-Olson (FMO) complex. We show that TDVP-MU and TDVP-PS yield the
same result when the time step size is converged and they are more accurate
than P&C-RK4, while TDVP-PS tolerates a larger time step size than TDVP-MU. We
further adopt the graphical processing units (GPU) to accelerate the heavy
tensor contractions in TD-DMRG and it is able to speed up the TDVP-MU and
TDVP-PS schemes by up to 73 times.
