论文标题
通过分区和缩放采样系统地降低蒙特卡洛计算的缩放
Systematic lowering of the scaling of Monte Carlo calculations by partitioning andsubsampling
论文作者
论文摘要
我们建议使用条件期望值通过蒙特卡洛计算来计算物理特性。后者是通过在几个子空间或片段中划分的物理空间，并在冷冻环境的同时对每个片段（即执行侧面步行）进行分区，从而在通常的Monte Carlo取样上获得。没有引入偏差，零变化原理在可分离性的极限中，即碎片是独立的。在实践中，蒙特卡洛计算的通常瓶颈 - 统计波动的缩放是粒子n数量的函数 - 可缓解广泛的可观察结果。我们使用jastrow-slater波函数说明了2D哈伯德模型上的变异蒙特卡洛和金属氢链上的方法。一个因子O（n）以数值效率获得。
We propose to compute physical properties by Monte Carlo calculations using conditional expectation values. The latter are obtained on top of the usual Monte Carlo sampling by partitioning the physical space in several subspaces or fragments, and subsampling each fragment (i.e., performing side walks) while freezing the environment. No bias is introduced and a zero-variance principle holds in the limit of separability, i.e. when the fragments are independent. In practice, the usual bottleneck of Monte Carlo calculations -- the scaling of the statistical fluctuations as a function of the number of particles N -- is relieved for extensive observables. We illustrate the method in variational Monte Carlo on the 2D Hubbard model and on metallic hydrogen chains using Jastrow-Slater wave functions. A factor O(N) is gained in numerical efficiency.
