A Mixed-Precision Implementation of the Density Matrix Renormalization Group

Abstract

Using the mixed precision strategy to optimize quantum chemistry codes has been proved promising in saving computational cost and maintaining chemical accuracy. Here, an efficient mixed-precision density matrix renormalization group (DMRG) scheme, containing a two-level mixed-precision hierarchy, is developed and demonstrated. At the coarse-grained level, based on the discovery that the single-precision orthogonalization may cause the DMRG generate a totally wrong answer, a feasible single-precision-sweep DMRG method with double-precision orthogonalization process is implemented. At the fine-grained level, a mixed-precision diagonalization algorithm is developed. This algorithm runs specific operations in the single-precision while preserving double-precision accuracy. Combining these two method, a hybrid mixed-precision scheme is presented. By applying this scheme, the DMRG single-point energy calculations are accelerated up to 131%. Mixed-precision DMRG yielded energies are accurate and deviate less than 0.01 kcal/mol compared with standard DMRG calculations.