Scott Charles J C, Di Remigio Roberto, Crawford T Daniel, Thom Alex J W
Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom.
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway.
J Chem Phys. 2020 Oct 14;153(14):144117. doi: 10.1063/5.0026513.
We present a detailed discussion of our novel diagrammatic coupled cluster Monte Carlo (diagCCMC) [Scott et al. J. Phys. Chem. Lett. 10, 925 (2019)]. The diagCCMC algorithm performs an imaginary-time propagation of the similarity-transformed coupled cluster Schrödinger equation. Imaginary-time updates are computed by the stochastic sampling of the coupled cluster vector function: each term is evaluated as a randomly realized 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 realization 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, independent of the truncation level in coupled cluster theory. The algorithm only requires an asymptotic memory cost scaling linearly, as demonstrated previously. These scaling reductions require no ad hoc modifications to the approach.
我们详细讨论了我们新颖的图解耦合簇蒙特卡罗方法（diagCCMC）[斯科特等人，《物理化学快报》10, 925 (2019)]。diagCCMC算法对相似变换后的耦合簇薛定谔方程进行虚时传播。虚时更新通过耦合簇向量函数的随机抽样来计算：每一项都被评估为相似变换哈密顿量的连通展开中随机实现的图。当将确定性和随机链接耦合簇理论重新表示为图解展开的抽样时，我们突出了它们之间的异同，并讨论了我们实现方式的细节，这种实现方式允许无游走者的随机抽样。最后，我们证明，在存在局域性的情况下，我们的算法可以为每个电子获得固定的误差条，同时只需要与系统大小成四次方比例的渐近计算量，与耦合簇理论中的截断水平无关。如前所示，该算法仅需要线性缩放的渐近内存成本。这些缩放降低不需要对该方法进行特别修改。
