Diagrammatic Coupled Cluster Monte Carlo

Abstract

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach -- diagCCMC -- allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems, diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches.

31 pages, 6 figures

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• A Stochastic Approach to Unitary Coupled Cluster
• Preconditioning and perturbative estimators in full configuration interaction quantum Monte Carlo
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• Multireference Stochastic Coupled Cluster
• Stochastic many-body perturbation theory for electron correlation energies
• Theory and Implementation of a Novel Stochastic Approach to Coupled Cluster
• Accelerating Stochastic Quantum Chemistry
• Exploration of interlacing and avoided crossings in a manifold of potential energy curves by a Unitary Group Adapted State Specific Multi-Reference Perturbation Theory (UGA-SSMRPT)
• Diagrammatic Monte Carlo for electronic correlation in molecules: high-order many-body perturbation theory with low scaling