The 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 the TD-DMRG, the global propagation and compression method with the Runge-Kutta algorithm (P&C-RK), the time dependent variational principle based methods with the matrix unfolding algorithm (TDVP-MU), and with the projector-splitting algorithm (TDVP-PS), by performing benchmarks on the exciton dynamics of the Fenna-Matthews-Olson 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 to accelerate the heavy tensor contractions in the TD-DMRG, and it is able to speed up the TDVP-MU and TDVP-PS schemes by up to 73 times.

中文翻译：

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TD-DMRG时间演化方案的准确性和GPU加速的数值评估。

时间依赖性密度矩阵重归一化组（TD-DMRG）已成为复杂系统量子动力学的前沿方法之一。在本文中，我们比较研究了TD-DMRG中三种时间演化方案的准确性，采用Runge-Kutta算法（P＆C-RK）的全局传播和压缩方法，基于时间依赖变分原理的方法以及矩阵展开算法的准确性。 （TDVP-MU）和投影仪分离算法（TDVP-PS），通过对Fenna-Matthews-Olson复合体的激子动力学进行基准测试。我们显示出，当时间步长收敛时，TDVP-MU和TDVP-PS产生相同的结果，并且它们比P＆C-RK4更精确，而TDVP-PS容忍的时间步长比TDVP-MU大。