Another interesting phenomenon observed in the figures is that, in general, the speedup of single-precision sweep method is higher than the speed-up of the mixed-precision diagonalization method. This is reasonable, that for the coarse-grained level method, most operations including the diagonalization, the SVD decomposition and the update of the ENV are transformed into single-precision mode. However, in the fine-grained level method, only several iterations of the diagonalization procedure are transformed. Hence, the coarsegrained level method is naturally and rightfully achieved a higher speed-up than the finegrained level method when there is no convergence issue in diagonalization. To finish this section, we would like to investigate the convergence behavior in the DMRG sweep of the mixed-precision scheme at different circumstances. The benzene molecule was chosen as an example. The total number of sweeps to convergence for different active space in DMRG calculations. Therefore, the combination of these two methods is essential to construct a high accuracy and high performance mixed-precision DMRG scheme.