一种新的耦合聚类随机方法的理论与实现
Theory and Implementation of a Novel Stochastic Approach to Coupled Cluster
摘要：
我们提出了一个详细的讨论，我们的新的图形耦合簇蒙特卡罗（diagCCMC）[斯科特等人，物理化学快报。2019，10，925]。diagCCMC算法执行相似变换的耦合簇薛定谔方程的时间-时间传播。虚时更新计算随机采样的耦合集群向量函数：每个术语被评估为一个随机实现的图中的相似变换的哈密顿连接扩展。我们强调确定性和随机链接耦合集群理论之间的相似性和差异时，后者被重新表示为一个采样的图形扩展，并讨论我们的实施细节，允许一个步行者少实现的随机采样。最后，我们证明，在局部性的存在下，我们的算法可以得到一个固定的errorbar每个电子，而只需要一个渐进的计算工作，规模与系统大小的四次方，独立于截断水平耦合集群理论。该算法只需要一个渐进的内存成本线性缩放，如前所述。这些比例缩减不需要对方法进行特别修改。
英文摘要：
We present a detailed discussion of our novel diagrammatic coupled cluster Monte Carlo (diagCCMC) [Scott et al. J. Phys. Chem. Lett. 2019, 10, 925]. The diagCCMC algorithm performs an imaginary-time propagation of the similarity-transformed coupled cluster Schrödinger equation. Imaginary-time updates are computed by stochastic sampling of the coupled cluster vector function: each term is evaluated as a randomly realised diagram in the connected expansion of the similarity-transformed Hamiltonian. We highlight similarities and differences between deterministic and stochastic linked coupled cluster theory when the latter is re-expressed as a sampling of the diagrammatic expansion, and discuss details of our implementation that allow for a walker-less realisation of the stochastic sampling. Finally, we demonstrate that in the presence of locality, our algorithm can obtain a fixed errorbar per electron while only requiring an asymptotic computational effort that scales quartically with system size, independently of truncation level in coupled cluster theory. The algorithm only requires an asymptotic memory costs scaling linearly, as demonstrated previously. These scaling reductions require no ad hoc modifications to the approach.
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