Analysis of pseudo-random number generators in QMC-SSE method

In the quantum Monte Carlo (QMC) method, the pseudo-random number generator (PRNG) plays a crucial role in determining the computation time. However, the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process. Here, we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion (SSE) algorithm. To quantitatively compare them, we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms. After testing several representative observables of the Heisenberg model in one and two dimensions, we recommend the linear congruential generator as the best choice of PRNG. Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.