标题： 变分和扩散蒙特卡罗方法简介 显示英文标题

标题： Introduction to the variational and diffusion Monte Carlo methods

摘要： 我们提供了一篇教学性的介绍，阐述了用于电子结构计算的实空间量子蒙特卡罗方法的两种主要变体：变分蒙特卡罗（VMC）和扩散蒙特卡罗（DMC）。 假设对这一主题没有先验知识，我们深入回顾了在VMC中用于采样近似波函数平方的Metropolis-Hastings算法，讨论了对电子系统应用至关重要的细节。 我们还详细回顾了在固定节点近似下引入的更复杂的DMC算法，该算法用于避免著名的费米子符号问题，从而使人们能够采样更精确的基态波函数近似值。 在整个综述过程中，我们讨论了用于评估期望值和统计不确定性的统计方法。 特别是，我们展示了如何估计期望值的非线性函数及其统计不确定性。 显示英文摘要

摘要： We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on the subject, we review in depth the Metropolis-Hastings algorithm used in VMC for sampling the square of an approximate wave function, discussing details important for applications to electronic systems. We also review in detail the more sophisticated DMC algorithm within the fixed-node approximation, introduced to avoid the infamous Fermionic sign problem, which allows one to sample a more accurate approximation to the ground-state wave function. Throughout this review, we discuss the statistical methods used for evaluating expectation values and statistical uncertainties. In particular, we show how to estimate nonlinear functions of expectation values and their statistical uncertainties.