Mixed Granularity Parallelization Scheme for Determinant Quantum Monte Carlo Simulations

With the ability to reveal the macroscopic properties of correlated electron systems, Determinant Quantum Monte Carlo (DQMC) simulations is a popular method in condense matter physics. Studies of emerging complex materials eagerly demand more computational powers to carry out the simulations. However, parallelization of the DQMC simulation is extremely challenging, owing to the serial nature of underlying Markov chain theory and numerical stability issues. Here, we present a mixed granularity parallelization (MGP) scheme that combines algorithmic and implementation techniques to speed up DQMC simulations. Some of these are novel and some extendend earlier work. From coarse grained parallel Markov chain and task decompositions to fine grained parallelization methods for Green’s function calculation and matrix computations, the MGP scheme explores the parallelism on different levels of simulations and maps the algorithms to suitable computational components on modern high performance computer systems. Practical techniques, such as communication and computation overlapping, message compression and load balance are also considered in the MGP scheme. We had implemented the MGP scheme on the Blue Gene/P. The effectiveness of the new scheme is justified through both theoretical analysis and performance results. Experiments had shown significant speedup on thousands computation nodes.