基于涨落坐标标度的路径积分维里估计：在四阶传播子量子团簇中的应用
Path integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators
摘要：
我们首先表明，根据给定的参考点定义的波动坐标的简单缩放给出了离散路径积分中的常规维里估计，其中参考点的不同选择导致不同形式的估计（例如，质心维里）。这个过程的优点是，它允许一个有限差分评估的维里估计相对于温度，这完全避免了需要高阶潜在的衍生物。我们将此方法应用于（H_2）_22和Ne_（13）团簇的能量和热容的计算。如果使用解析维里估计，这种类型的计算需要高达三阶的势能导数，但在实践中，凭借上述有限差分格式，仅一阶导数就足够了。从量子团簇的应用中，我们发现四阶传播子确实改善了原始近似，并且参考点的选择在减少维里估计的方差方面起着至关重要的作用。
英文摘要：
We first show that a simple scaling of fluctuation coordinates defined in terms of a given reference point gives the conventional virial estimator in discretized path integral, where different choices of the reference point lead to different forms of the estimator (e.g., centroid virial). The merit of this procedure is that it allows a finite difference evaluation of the virial estimator with respect to temperature, which totally avoids the need of higher-order potential derivatives. We apply this procedure to energy and heat capacity calculation of the (H_2)_22 and Ne_13 clusters at low temperature using the fourth-order Takahashi-Imada and Suzuki propagators. This type of calculation requires up to third-order potential derivatives if analytical virial estimators are used, but in practice only first-order derivatives suffice by virtue of the finite difference scheme above. From the application to quantum clusters, we find that the fourth-order propagators do improve upon the primitive approximation, and that the choice of the reference point plays a vital role in reducing the variance of the virial estimator.
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