From these two tables, we can infer that the mixed-precision diagonalization method performed better than other two methods for the Cr 2 system, while the hybrid mixed- precision scheme, combining both single-precision sweep and mixed-precision diagonalization, performed better than other two methods for the benzene system. For the Cr 2 system, the full single-precision DMRG may yield inaccurate energy, and have a poor performance improvement. The reason is, as said in the previous paragraph, that the single-precision diagonalization process has a big convergence issue. In each sweep, the total iteration number for diagonalization in single-precision is much larger than in double-precision. For example, on site 16, double-precision diagonalization took 15 iterations with 295.7 seconds, comparing to 31 iterations for the single-precision diagonalization, consuming 314.8 seconds. Hence, the speed-up for single-precision sweep method in one sweep is much lower. On the contrary, a 2.21 speed-up for the same method in one sweep is achieved when there is no convergence issue in the benzene system test. This convergence issue also effected the total number of sweeps. The double-precision DMRG method converged in 10 sweeps, while the hybrid mixed-precision scheme, and the single-precision sweep approach converged in 12 sweeps.