Theory and Implementation of a Novel Stochastic Approach to Coupled Cluster

Abstract

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.

References in corpus (24)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Applications of quantum Monte Carlo methods in condensed systems
• Semistochastic Projector Monte Carlo Method
• Diagrammatic Monte Carlo
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method
• Semi-stochastic full configuration interaction quantum Monte Carlo: developments and application
• High-Performance Tensor Contraction without Transposition
• Developments in Stochastic Coupled Cluster Theory: The initiator approximation and application to the Uniform Electron Gas
• Quantum Monte Carlo calculations of energy gaps from first principles
• The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up
• Time-dependent coupled-cluster method for atomic nuclei
• Exciting determinants in Quantum Monte Carlo: Loading the dice with fast, low memory weights
• Stochastic Coupled Cluster Theory: Efficient Sampling of the Coupled Cluster Expansion
• A study of the dense Uniform Electron Gas with high orders of Coupled Cluster
• Linked Coupled Cluster Monte Carlo
• Preconditioning and perturbative estimators in full configuration interaction quantum Monte Carlo
• Multi-state effective Hamiltonian and size-consistency corrections in stochastic configuration interactions
• Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra
• Clustered Low-Rank Tensor Format: Introduction and Application to Fast Construction of Hartree-Fock Exchange
• Diagrammatic Coupled Cluster Monte Carlo
• Accelerating Stochastic Quantum Chemistry
• Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error using Fast Randomized Iteration
• Efficient Electronic Structure Theory via Hierarchical Scale-Adaptive Coupled-Cluster Formalism: I. Theory and Computational Complexity Analysis

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