Analysis of Pseudo-Random Number Generators in QMC-SSE Method

Abstract: 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 the different PRNGs on the widely used QMC method -- 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 using LCG as the best choice of PRNGs. Our work can not only help improve the performance of the SSE method but also shed light on the other Markov-chain-based numerical algorithms.