论文标题
晶格场理论的蒙特卡洛采样中的无限差异
Infinite Variance in Monte Carlo Sampling of Lattice Field Theories
论文作者
论文摘要
在晶格量子场理论中期望值的蒙特卡洛计算中，所使用的采样过程的随机方差定义了固定数量样品的计算精度。如果特定数量的估计器的方差正式无限，或者在实践中与均值平方相比非常大，则无法使用给定采样程序可靠地估计该数量。在多种情况下，其中包括在晶格量子染色体动力学中，一个特别简单的示例是由gross-neveu模型给出的，其中蒙特卡洛计算涉及通过Hubbard-Stratonovich（HS）转换引入辅助玻璃体变量。在这里，可以表明，在此模型中，涉及费米昂字段的运算符类别的HS估计量和更简单的零维模拟都存在分歧。为了正确估计这些可观察到的物品，提出了两种替代抽样方法并通过数值研究。
In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of an estimator of a particular quantity is formally infinite, or in practice very large compared to the square of the mean, then that quantity can not be reliably estimated using the given sampling procedure. There are multiple scenarios in which this occurs, including in Lattice Quantum Chromodynamics, and a particularly simple example is given by the Gross-Neveu model where Monte Carlo calculations involve the introduction of auxiliary bosonic variables through a Hubbard-Stratonovich (HS) transformation. Here, it is shown that the variances of HS estimators for classes of operators involving fermion fields are divergent in this model and an even simpler zero-dimensional analogue. To correctly estimate these observables, two alternative sampling methods are proposed and numerically investigated.
