end while 21: end procedure With the combination of both the coarse-grained level method and the fine-grained level method, we can construct a hybrid mixed-precision scheme. For this hybrid scheme, the DMRG calculation starts with the single-precision sweep. After several sweeps, it reaches the single-precision convergence point. Consequently, the data is transformed into doubleprecision. Subsequenly, the mixed-precision diagonalization method is applied until the required accuracy is reached. A simplified flow chart of this hybrid scheme is illustrated in 3 Result and discussion