Effective Parallelization of Quantum Simulations: Nanomagnetic Molecular Rings

Abstract

AbstractThe effective parallelization of processing exploiting the MPI library for the numerically exact quantum transfer matrix (QTM) and exact diagonalization (ED) deterministic simulations of chromium-based rings is proposed. In the QTM technique we have exploited parallelization of summation in the partition function. The efficiency of the QTM calculations is above \(80\,\%\) up to about \(1000\) processes. With our test programs we calculated low temperature torque, specific heat and entropy for the chromium ring Cr\(_8\) exploiting realistic Hamiltonian with single-ion anisotropy and the alternation of the nearest neighbor exchange couplings. Our parallelized ED technique makes use of the self-scheduling scheme and the longest processing time algorithm to distribute and diagonalize separate blocks of a Hamiltonian matrix by slave processes. Its parallel processing scales very well, with efficiency above \(90\,\%\) up to about 10 processes only. This scheme is improved by processing more input data sets in one job which leads to very good scalability up to arbitrary number of processes. The scaling is improved for both techniques when larger systems are considered.KeywordsParallelization of processingMPINumerical simulationsNanomagnetic ringsHeisenberg model