update ENV ▷ S 28: end for After the single-precision sweep converged, the single-precision data (MPO, MPS and ENVs) are transformed into double precision. Subsequently, the double-precision sweep starts as in a standard DMRG calculation. The only remaining question is to determine the switching point of these mixed-precision scheme, i.e. how to determine the convergence of the single-precision sweep. According to the IEEE 754 standard, the 32-bit floating point data form has a relative error of around 10 -7 . Thus the convergence threshold of the single-precision sweep is around 10 -4 -10 -5 , based on the different systems. However a manually-appointed threshold number is unascertainable. Consequently, we choose another way to determine the convergence. In the first several single-precision sweep, the energy sustains to decrease sweep by sweep. But when the convergence point is reached, the energy starts to fluctuate. Therefore, if the energy of the current sweep is larger than the last sweep, one can determine that the convergence point has been reached.