论文标题
用于推断耦合簇相关能量到热力学极限的功率定律
Power laws used to extrapolate the coupled cluster correlation energy to the thermodynamic limit
论文作者
论文摘要
使用耦合簇在固体上的最新计算提出了讨论，讨论了使用$ n^{ - 1/3} $ power Law在外推到热力学极限时适合相关能量，这种方法与更常用的$ n^{-1} $ power Law（例如（例如）（例如，（例如）经常使用的量子Monte Monte Carlo方法通常使用。在本文中，我们提出了一种调和这些观点的方法。对非常广泛的密度范围（$ 0.1 <r_s <100.0 $），对达到$ 922 $电子的均匀电子气体进行了耦合群集双打计算，以研究相关能量如何接近热力学极限。纠正数据以设置不完整的误差，并使用选定的扭角方法来减轻壳填充效果的有限尺寸误差。分析这些数据时，我们最初发现$ n^{ - 1/3} $的功率定律似乎比$ n^{ - 1} $ Power Law在大型系统尺寸限制中更适合数据。但是，我们提供了过渡结构因子的分析，表明$ n^{ - 1} $仍然适用于大型系统尺寸，并且显而易见的$ n^{ - 1/3} $ Power Law仅出现在低$ n $下。
Recent calculations using coupled cluster on solids have raised discussion of using a $N^{-1/3}$ power law to fit the correlation energy when extrapolating to the thermodynamic limit, an approach which differs from the more commonly used $N^{-1}$ power law which is (for example) often used by quantum Monte Carlo methods. In this paper, we present one way to reconcile these viewpoints. Coupled cluster doubles calculations were performed on uniform electron gases reaching system sizes of $922$ electrons for an extremely wide range of densities ($0.1<r_s<100.0$) to study how the correlation energy approaches the thermodynamic limit. The data were corrected for basis set incompleteness error and use a selected twist angle approach to mitigate finite size error from shell filling effects. Analyzing these data, we initially find that a power law of $N^{-1/3}$ appears to fit the data better than a $N^{-1}$ power law in the large system size limit. However, we provide an analysis of the transition structure factor showing that $N^{-1}$ still applies to large system sizes and that the apparent $N^{-1/3}$ power law occurs only at low $N$.
